Furthermore, why do we today treat Henry VII and William the Conqueror as completely different (We literally start the counting of English kings from William I and ignore the anglo-saxon kings before him), when they seem to be so similar?
Both were related to the ruling line, but not descended from it (William being Edward the Confessor's cousin, and Henry VII being Henry VI's half-brother), both won the throne on the battlefield in spite of a very questionable blood claim, and both worked to legitimize their claim through marriage (to Matilda in the case of William's son Henry I, and to Elizabeth of York in Henry VII's case.) Yet, we don't restart the counting of kings with Henry Tudor.
Partly that was deliberate policy on behalf of the Tudors. While their claim could be considered tenuous at best, this did not stop Henry from spending a lot of energy legitimising his reign. In fact it could be argued that it was the fear of their soft claim to power that drove his son, Henry, to such extremes when it came to securing a male dynastic heir.
As for why both Henry VII and William of Normandy did not ‘year zero’ either of their reigns the answer is very simple. Politics.
In both cases the two men sought to claim an existing title; in both cases their claim was weak but justified by force of arms; and in both cases true legitimacy was gained through the majesty of the office.
Had either man had of tried to place themselves without the long roots of previous sovereigns as legitimacy, it could be argued they would have both faced much more conflicted reigns.
Henry VII was especially brilliant in what he did. He gasped quickly the power of propaganda, producing ornate and elaborate genealogies that legitimised his claim (and therefore the claims of his heirs) and he unleashed powerful iconography (the utterly made up symbol of the Tudor Rose- it could be argued that the entire War of the Roses narrative was given shape in order to give post-hoc justification to the Tudors, certainly the Red Rose wasn’t widely used in the preceding decades).
The Tudors were lucky to a degree; Henry came to power during an era of great societal change, with everything up for grabs. This is why the role of the nobility was weakened by Henry, as these were not just a threat but a throwback to the previous Plantagenet regimes. It was also the era when England underwent a huge economic change as the focus shifted (due to the pressures caused by the end of the 100 Years War and the rise of the Hansa) towards London and the south-east.
There was a wider sense of change in the air and the new monarch encapsulated this, allowing him to audaciously claim legitimacy while also usurping the longest running, most successful dynasty England ever had.
Consider also the turmoil and conflict that England had just experienced during the death rattle of the Plantagenet Dynasty; the chaos of competing kings, changing political fortunes, bloodshed and death meant there was a palpable desire for someone, anyone, to bring peace.
He dated his reign from the day before his final battle with Richard III (allowing it be seen that he was already King when he won and it was ordained by God). An epidemic of sweating sickness in London delayed his actual coronation for a couple of months and this allowed Henry (who had after all spent most of his life abroad and preferred to speak French) to use the one weapon open to him- lacking any kind of political capital within Britain, he used pageantry to LOOK the part of the King.
By all accounts this lavish and grandiose affair did the trick, at least in the short term. The crucial key to his gaining the throne however was his marriage to Elizabeth, eldest daughter of Edward IV. It was their union that saw the Tudor Rose begin to be used as a symbol not just of a marriage but to grant visual legitimacy to Henry’s rule.
Simply put- the symbology of that red and white rose said: All the fighting and division that the nation had just been through for decades was down to the division of those two roses, and with their union, the division was over.
Simplistic, revisionist, utterly political and basically the successful message Henry got across. This idea still is perceived as why the Tudors took over, basically saying that Henry’s selective re-editing of history was successful.
Yet he never felt secure, never truly rested. A small number of ‘claimants’ as well as surviving Plantagenets, always worried him. Ultimately the Tudor dynasty was secured by Henry basically killing any rival to his house.
We today don’t restart the Kings because the monarchs of England/Britain gain legitimacy via the majesty of the heritage of the crown. It has allowed every usurping dynasty (be it Godwinsun, Normandy, Tudor, Orange or Hannover) to be clothed in that very legitimacy. Maintaining the line of Kings is good politics.
After all, the only regime change that ended the cycle also did so for political reasons (the Commonwealth/Protectorate).
Hope that helps.
Couple of good sources for this stuff:
-André, B. The Life of Henry VII, trans D Hobbins; New York; 2011
-Jones, Dan. The Hollow Crown; London; 2014
If you want to find deeper stuff I can suggest a few others.