Sorry for really late response.
In short, the opinions of researchers in the last 40 years on OP's question (especially the first part) has largely divided into the following two factors, though almost all the researches agree that both factors played somewhat important role in Cnut's (and his father Sweyn's as well) success to rule the territories around the North Sea. What they haven't reached an agreement is the balance between the two factors, namely 'English' element and 'Scandinavian' element, to put different component of 'the Empire' together under his auspice.
1: 'English' element of his reign: England as a source of wealth and technocrats
The traditional (up to [Lawson 1993]) view on Cnut's Empire had primarily focused on his power base in England.
At the turn of the millennium, England under Aethelred II (ca. 1000) was probably the richest kingdom with the most effective administrative institution in contemporary Latin West. The scribe of Anglo-Saxon Chronicle (MS D) states in the entry of 1018 CE that the English people paid 82,500 pounds (including the 10,000 pounds from the Londoner) to Cnut and his expedition army in this year alone (Swanton trans. 2000: 154). 82,500 Pounds amount to ca. 28.875 tons of silver. Lawson calculates that at least 240,500 Pounds (ca. 84 tons of silver) in total paid as tribute to the Viking fleets under the reign of Aethelred and early years of Cnut (991-1018), but this payment of the year 1018 by far the largest for the single year (Lawson 1993: 189-91).
Cnut distributed much of this payment to his (and his father's) former followers to disband the majority of the expedition fleets (only 40 ships left). By the power of this extraordinary power of money (wealth), he brought relative peace with much less Viking ships in his dominion across the North Sea. In other words, the traditional view sees him primarily as a very rich Dane ex-Viking ruler sitting on the English throne, the most convenient source of wealth in the early 11th century.
In addition to this payment, sometimes called as 'Danegeld', the Anglo-Saxon fiscal (coinage) system wielded further additional wealth to Cnut. Late Anglo-Saxon and Anglo-Norman England since the reign of King Edgar (r. 959-975) was one of the few kingdoms in contemporary west that the kingship could have the tight control of the coinage and the circulation of money within his kingdom. Even regular re-coinage with tightly controlled dies and moneyers enabled the ruler to make profit from the handling charge of exchange with new type of coins.
It is often pointed out now, however, that Cnut invited the Anglo-Saxon moneyer into Denmark to 'modernize' the currency system, though the different weight/ standard between England and Denmark suggests that he could not build the unified economic bloc across his empire (Jonsson in Rumble ed. 1994: 230). The Danish coinage system imitated the English one, but foreign coins from Germany still also flowed in Denmark in not so small amount that the kingship could not totally monopolize the control of the circulation of money there.
The similar pattern also applied to the clergy of the developing Danish church. Sweyn Forkbeard and his son Cnut preferred the Anglo-Saxons to the German protege of the archbishop of Hamburg-Bremen, as bishops in their kingdom of Denmark. While Anglo-Saxons who had come to Scandinavia would occupy the strategically important bishops like Lund in eastern Denmark up to ca. 1060s, Cnut had met a strong resistance from the archbishop of Hamburg-Bremen in Germany who had claimed the exclusive privileges of the mission in Northern-Europe. Archbishop of Hamburg-Bremen once even succeeded in taking Anglo-Saxon Bishop Gerbrand of Roskilde (Cnut's protege in Danish church) into captivity and making him the fealty to the German archbishop himself. Researchers has not reached an agreement, however, to what extent either kings of Denmark or archbishop of Hamburg-Bremen had the actual control of the circumstances in the church and missionary scenes in Scandinavia.
Thus, as for both the coinage and Christianity, Cnut had much favorable positions than his potential political rivals in Scandinavia like Olaf Haraldsson of Norway (d. 1030) to invite Anglo-Saxon experts to introduce the 'advanced' machinery of English (Anglo-Saxon) style of the administration, due to his rule in England, though how much exactly he controlled the whole situation could be debated. Bolton suggests in his latest biography on Cnut, however, that not only named high-ranking officials, but also English commoner town-dwellers like merchants also came to live in emerging Danish cities, just as I mentioned recently for the Slavs (Wends) in some Danish cities about the same time here, mainly based on archaeological finds from the town landscape (Bolton 2017: 144; Id. 2009: 220-25).
2: 'Scandinavian' element of his reign: 'indirect' rule in Scandinavia by way of local magnates and personnel networks
By comparing two recent biographies on Cnut, especially the first edition of [Lawson 1993] and the latest [Bolton 2017] or its predecessor monograph [Bolton 2009], it it clear that more and more pages and attention has been paid to fragmentary traces of his 'policy' in Scandinavian part of the Empire, based on the limited amount of contemporary written and non-written sources like runic inscriptions as well as numismatic sources as well. What could he rely on the indirect rule in Scandinavia on behalf of himself, without the effective administrative machinery as those of Anglo-Saxon counterpart?
Untimely death of his brother Harald in Denmark in 1018 could, in a sense, be a providential help as well as the curse for Cnut's rule across the North Sea: While this incident certainly enabled the personal union of England and Denmark, it also robbed him of the most reliable political ally in Scandinavia (Bolton 2017: 132). Then, who were to be chosen as his 'regent' in Denmark-Scandinavia? Or, was just a single 'regent' enough to rule not only Denmark, but also over the Scandinavian world in a wider context?
Cnut's grandfather Harald (Bluetooth) and father Sweyn (Forkbeard) of the Jelling dynasty of the Danes had mainly made use of political marriage to stabilize the politics around Scandinavia and the Baltic: Harald and possibly also Sweyn took his wife from the duchy family of emerging Poland, and the (second?) wife of the latter [Sweyn] could also be a widow of King Eric the Victorious of the Svears (d. 995). By these political marriages, they could secure at least the potential support from the Baltic (note that Harald's last political refuge after his son (Sweyn)'s revolt was in southern Baltic, see this news article). On the other hand, Cnut himself had already 'spent' this resource to focus on the stabilization of his rule in England: Both of his spouses, Ælfgifu of Northampton and Emma of Normandy (widow of late King Aethelred II of England) came from the British-Norman milieu.
Cnut' troublesome dealings with Scandinavian, especially Danish non-royal magnates up to the middle of the 1020s represent these difficult circumstances in Scandinavia. Thorkell the tall, as famous as he also appeared in Japanese manga/ anime Vinland Saga series, was not definitely negligible political figure even after the establishment of Cnut's rule in England, since Anglo-Saxon chronicles (especially its manuscript C) relate the interesting record of the tension between Cnut and him. In 1021, Cnut sentenced outlawry to Thorkell and his family, but MS C also tells in its entry of 1023 that he admitted to entrust Thorkell and his son to guard Denmark, with the exchange of their sons to guarantee the settlement (Swanton trans. 2000: 157). While we don't know much further on this event from reliable contemporary accounts (this was indeed the last account of Thorkell in contemporary historical writings), Bolton tries to reconstruct this conflict, proposing an interesting hypothesis that Thorkell was then the earl (ON jarl) of Skåne in eastern Denmark and had married with the daughter of late King Aethelred of England (i.e. negligent to get Cnut's consent (Bolton 2009: 211-14, 218), coupling with Cnut's hypothetical campaign into the Baltic in the beginning of the 1020s to shutter the interests of Thorkell's supporter. Anyway, it was clear that Cnut could not officially rob Thorkell of all his former political power as well as alliance (so that they formally reconciled).
The second Danish magnate as well as regent of Denmark, Ulf, was probably no less troublemaker for Cnut. Some researchers even suppose that he indeed defied against Cnut in the middle of 1020s, in spite of his marriage with Cnut's sister, Estrid. The later tradition elaborated his death in Roskilde, as instructed by Cnut himself as a political assassination (Cf. Keynes in Rumble ed. 1994: 62-64). He also had a brother named Eilífr (Anlaf) who also served Cnut, but his fate as well as political loyalty was also not evident in contemporary sources.
[Continued to be part 2]
References:
+++
So the"North Sea Empire" was the brief moment in time where theoretically the Scandinavian realms of Norway, Denmark, and parts of Sweden, were ruled alongside the kingdom of England and parts of what is today modern Scotland by one person, Cnut/Knutr/Canute/Knud/Knut etc... (I tend to favor Canute the Great, so I'll stick with that)
This period in time was rather brief, Canute reigned as king in all of the various kingdoms as a whole for only seven years (1028 was when Norway submitted to his rule and he died in 1035) and after his death, the kingdoms that composed the so-called empire were divided as a matter of practicality (England and Denmark were briefly united again under Canute's son, also named Canute, though often referred to as Harthacnut) and Norway, Denmark, and England all drifted apart from each other. Part of this was down to succession, in theory Canute's youngest son, Harthacnut, would rule all of the realms as one with his brothers ruling as regents in his absence. This would not have been an unusual arrangement as a king could not be in all three kingdoms at once and it was often necessary to have someone there to keep an eye on untrustworthy lords and magnates who would like nothing better than the chance to shove off their obligations to the king. However this system was intended to work, it did not come to fruition, and brace yourself because this gets a little complicated.
Upon Canute's death, his son Harthacnut was the theoretical heir to both England and Denmark (due to his mother Emma of Normandy being married to the prior king of England, Edmund Ironside, and consequently favored to succeed in England and promised the throne in Denmark as well) but he was occupied in Denmark at the time as Magnus the Good of Norway had recently deposed Canute's eldest son Sweyn (who had been ruling in Norway as his father's regent) and was making headway against Harthacnut's rule in Denmark.
Consequently Canute's other son, (though second oldest) named Harold, was made regent in England in Harthacnut's absence. Harold however was unpopular among the lords of southern England, especially with Earl Godwin, a powerful landowner and father to the future king Harold Godwinson, and this stymied his attempts to become sole king of England, instead he was ruling on behalf of his brother who was occupied in Denmark. At some point however Sweyn died in exile, never being crowned king in Norway, and Harold was able to coalesce support for himself to be proclaimed sole king in England. Harthacnut was unable to challenge this and never actively opposed his brother's ascent to the throne (or more likely was unable to do so). Harold's rule was still rather brief however and within only a few years of his father's death, Harold also passed. Harthacnut eventually did arrive in England to press his claim with an army, only to find that Harold died rather quickly of some disease. Harthacnut had his brother's body exhumed, beheaded, and unceremoniously thrown into a river where it was recovered and eventually buried. Harold left no legitimate children (he did have an illegitimate child who was shipped off to a monastery in France) and Harthacnut's eventual arrival with an army settled that succession dispute quickly.
However Harthacnut did not last long on both thrones either, and he too died young at the age of 24, having ruled Denmark and England jointly for only a few years. Prior to his death, he brought his half brother Edward (through their shared mother, Emma of Normandy) from exile in Normandy and he succeeded Harthacnut in England. Harthacnut was succeeded in Denmark by his old rival Magnus of Norway (Magnus fought with Harthacnut's cousin for the throne, and eventually Sweyn II of Denmark won control after Magnus lost sole rule in Norway to his uncle, Harald Hardaade.) In England Edward the Confessor would likewise die without issue, throwing that throne into contention between the Norwegians, Harold Godwinson, and Edward's cousin William the Bastard. In Denmark the descendants of Sweyn II ruled until the 14th century, and Norway was permanently lost to English rule (it would survive as an independent kingdom until the 13th century where afterwards it became a battleground between the Swedes and Danes)
This is a long winded way of saying that the reason the North Sea Empire did not last long, was that the successors to Canute all died relatively young and without legitimate heirs. Nor was the "empire" held together for very long in the first place, and certainly not without a great deal of effort. Canute had to see off revolts against his rule in Norway, Denmark, and England all at various times and ruling such large areas of land that were all separated by large tracts of sea was no easy feat to begin with. It was only held together, such as it was, through Canute's use of regents and military force to ensure his reign stayed.