The premise behind this question, I think, is just as important as the question itself, and I think that, when it's considered, the question answers itself (with some context). Why would the people of Rome revolt against Tiberius/Caligula/Nero?

This is very much going to be a historiography discussion, paired with a bit of history'n'stuff. The obvious reason that these three men were singled out as "emperors who ought to be revolted against" is due to a perspective that's given to the modern eye thanks to the surviving sources, none of which are particularly positive towards the men in question. Oftentimes, their antics are so over the top that any sane person ought to recoil in horror, indeed suggesting that said sane person must consider revolt against such a cruel, insane, and unjust person. But what these sources say rather than embellish is, perhaps, the most important clincher.

Perhaps the most (in)famous of the biographers is Suetonius, who gives any reader some delightful tidbits to devour, along with his overall view on the man in question. For Tiberius, he gleefully describes him as a hateful old man, cruel, sadistic, delighting in horrific sexual acts. Here's an example of such a quote (a bit extensive, but hey):

Moreover, having gained the licence of privacy, and being as it were out of sight of the citizens, he at last gave free rein at once to all the vices which he had for a long time ill concealed; and of these I shall give a detailed account from the beginning. Even at the outset of his military career his excessive love of wine gave him the name of Biberius, instead of Tiberius, Caldius for Claudius, and Mero for Nero. Later, when emperor and at the very time that he was busy correcting the public morals, he spent a night and two whole days feasting and drinking with Pomponius Flaccus and Lucius Piso, immediately afterwards making the one governor of the province of Syria and the other prefect of the city, and even declaring in their commissions that they were the most agreeable of friends, who could always be counted on. He had a dinner given him by Cestius Gallus, a lustful and prodigal old man, who had once been degraded by Augustus and whom he had himself rebuked a few days before in the senate, making the condition that Cestius should change or omit none of his usual customs, and that nude girls should wait upon them at table. He gave a very obscure candidate for the quaestorship preference over men of the noblest families, because at the emperor's challenge he had drained an amphora of wine at a banquet. He paid Asellius Sabinus two hundred thousand sesterces for a dialogue, in which he had introduced a contest of a mushroom, a fig-pecker, an oyster and a thrush. He established a new office, master of the imperial pleasures, assigning it to Titus Caesonius Priscus, a Roman knight.

On retiring to Capri he devised a pleasance for his secret orgies: teams of wantons of both sexes, selected as experts in deviant intercourse and dubbed analists, copulated before him in triple unions to excite his flagging passions. Its bedrooms were furnished with the most salacious paintings and sculptures, as well as with an erotic library, in case a performer should need an illustration of what was required. Then in Capri's woods and groves he arranged a number of nooks of venery where boys and girls got up as Pans and nymphs solicited outside bowers and grottoes: people openly called this "the old goat's garden," punning on the island's name.

He acquired a reputation for still grosser depravities that one can hardly bear to tell or be told, let alone believe. For example, he trained little boys (whom he termed tiddlers) to crawl between his thighs when he went swimming and tease him with their licks and nibbles; and unweaned babies he would put to his organ as though to the breast, being by both nature and age rather fond of this form of satisfaction. Left a painting of Parrhasius's depicting Atalanta pleasuring Meleager with her lips on condition that if the theme displeased him he was to have a million sesterces instead, he chose to keep it and actually hung it in his bedroom. The story is also told that once at a sacrifice, attracted by the acolyte's beauty, he lost control of himself and, hardly waiting for the ceremony to end, rushed him off and debauched him and his brother, the flute-player, too; and subsequently, when they complained of the assault, he had their legs broken.

So how could the people not hate such a person? Well, let's look at what Suetonius actually says about the man, rather than what he suggests. He notes that Tiberius went into private seclusion and was out of sight. The rest was certainly rumour at best, if not outright made up - there's no actual evidence to support any of this, and all of it is exactly the kind of thing that you'd expect people to rumour about a reasonably grouchy old man who decided that he'd had enough with Rome (he never liked it much throughout his entire life) and wanted to live in some semblance of peace and quiet. With regards to his administration of Rome, apart from Sejanus' attempted takeover, while he cut back on a number of building projects (certainly an unpopular policy in a city where a huge amount of income was based around construction work), he maintained the food supply, ensured that the Empire had a substantial bank at its disposal, and maintained peace throughout the Roman world. Trade with distant nations, especially India, boomed under his tenure, and people had luxuries that they'd never dreamed of having access to before (such as pepper). Games were still regularly sponsored, and the world was pretty good under Tiberius. Rumouring about the emperor getting up to progressively more terrible things was par for the course for a man who just wanted to be left alone.

His entire modus operandi was that he wanted to maintain the course and stick as faithfully to the law as possible. This, obviously, chafed quite a bit - and it certainly wasn't the best political position. As a result, he wasn't necessarily popular, but as he himself said, he'd prefer to be respected than to be popular. And, aside from the rumours, he was certainly well respected - his policies were carried out and he was heeded by those around him. With regard to his actual interests, there are a couple of quotes that I think are a bit more revealing about him as a human being:

He was greatly devoted to liberal studies in both languages. In his Latin oratory he followed Messala Corvinus, to whom he had given attention in his youth, when Messala was an old man. But he so obscured his style by excessive mannerisms and pedantry, that he was thought to speak much better offhand than in a prepared address. He also composed a lyric poem, entitled "A Lament for the Death of Lucius Caesar," and made Greek verses in imitation of Euphorion, Rhianus, and Parthenius, poets of whom he was very fond, placing their busts in the public libraries among those of the eminent writers of old; and on that account many learned men vied with one another in issuing commentaries on their works and dedicating them to the emperor. Yet his special aim was a knowledge of mythology, which he carried to a silly and laughable extreme; for he used to test even the grammarians, a class of men in whom, as I have said, he was especially interested, by questions something like this: "Who was Hecuba's mother?" "What was the name of Achilles among the maidens?" "What were the Sirens in the habit of singing?" Moreover, on the first day that he entered the senate after the death of Augustus, to satisfy at once the demands of filial piety and religion, he offered sacrifice after the example of Minos with incense and wine, but without a fluteplayer, as Minos had done in ancient times on the death of his son.

Looking past the clearly negative tones in there, the guy liked his oratory and poetry, and was devoted to trying to do things "the old way." Not only that, but he died at the ripe old age of 78 after an extended illness. Suetonius loves to say that "some people say that he was poisoned or murdered," but it's just as likely that....well....he died 'cause he was old.

So why not Caligula? I mean, he was clearly the worst, right? Well, some people certainly thought so, and those people were the reason that he was eventually murdered. But again, the things that are written about him are written by the same class of people who abhorred him so. While I certainly don't want to suggest that he was a blameless and delightfully decent human (probly not, it's hard to bankrupt a ridiculously huge surplus without being at least a bit of an ass), I, along with a decent number of modern historians, are of the opinion that he probably wasn't particularly insane. Nihilistic, perhaps, and with a sense of humour that obviously didn't go over particularly well, but not insane. Many of his projects seem to be tailored towards his being the "most popular kid in the class," and maintaining that "most popular kid" status by giving everyone everything that they wanted - he gave the people incredible amounts of massive construction projects, gave them constant grandiose games, created some of the most eyebrow-raising luxuries that are literally unimaginable before the modern-ish day, and threw huge, lavish festivals. When the money inevitably dried up, he took from the rich to continue them - again, not something that would induce said people to revolt.