This is slightly wrong. The crucial mistake in this is assuming that the Empire never existed without an Emperor. It simply isn't the case. The Roman Republic continued to be a Republic in name but became an Empire following the second Punic war. Rome's endless expansion had been ongoing, but without Carthage to counter Rome, Rome expansion ballooned. The deaths of most of the old lines in the various battles against Hannibal also meant that a new crop of politicians took over power, politicians that came to power through their amassed wealth, and who (pretty much immediately) turned the Republic into an oligopoly. At that point the patronage system became the only system: you had a patron, who gave you money to vote for what he wanted. Rome descended into practically rule of mob soon thereafter, which led to the rise of "populist" politicians, attempting to subvert the oligopoly via the Tribune of the Plebs veto (the only political position that still was voted primarily by the poor). The Gracae brothers being the most famous, but hardly the only ones.
In short: what killed the Roman Republic was expansion, yes, but the emperors (with a couple of minor exceptions) never expanded Rome. Because of this, emperors by and large were not scared of slaves, because without expansion, there weren't that many slaves (heck, the slaves run the Empire most of the time: ex-slaves formed the core of the bureaucracy under the more competent emperors). It was only the late Republic, the eternally expansionist one, that was awash with slaves from all the conquests and thus were the slave revolts happened (eventually forcing the Senate to pass laws to protect the slaves from abuse).
Grey Wolf