What is all this talk about the Republic being abolished? Just because we now have dictatorship-for-life doesn't make us any less a Republic! The Dictator serves the Senate and the People of Rome, after all. My fellow Romans, surely none of you would dare call our very Republican system... a monarchy? That kind of seditious talk is something I'd expect only from a Parthian spy!
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...but seriously, Caesar's fate in OTL does reveal that he'd made some serious errors in judgment when it came to forgiving certain enemies and expecting their forgiveness in turn, and more generally that he overestimated the security of his position. This is going to be a problem even if the plot on his life is somehow averted. For starters, even if the conspirators are somehow caught (rather than the whole thing being called off for now), Caesar must then choose between being very harsh and killing all serious enemies (which is what Augustus did in OTL), or again only kill the clear culprits and try to soothe all fence-sitters with his magnanimous attitude.
The former option will really harm his reputation, making all his enemies' accusations seem justified in hindsight Augustus in OTL played his mass murder very smartly, allowing his fellow Triumviri to indulge as well - even when it cost him friends - so that the blame was shared. He also had the advantage of later emerging victoriously out of a more 'honest' power struggle, and then had decades to have his people write the official histories. That's a pretty rare confluence of favourable conditions. Caesar might not be so lucky. Truly "cleaning house" might let him consolidate power during his life-time, but instead of, well, Caesar... history will mark him as a mass-murdering tyrant, while I bet his would-be assassins later get vindicated as the brave heroes who tried and failed to save the Republic.
The latter option, on the other hand, ensures that the underlying threat remains. Those who actually hate Caesar remain in positions of power, biding their time. And when he goes off on his Parthian campaign... well, the Dictator being very far away is a really good starting position for a coup at home, wouldn't you say? Gives you time to rally your forces for when he comes back.
And then there's the other option, which is simply that he invades Parthia and fails. He doesn't even have to die. If he does, we get something like OTL's succession struggles, but a bit later. But if he fails but survives, his reputation of glory is tarnished, making the aforementioned coup at home ever more likely...
Bottom line: historically speaking, Caesar's killers likely did him a favour. He died before he could mess things up. Sure, he might have lived on and succeeded in all he attempted, but the chances that things would have ended badly are considerably greater.