Would agree with this assessment that someone else simply takes Caesar's place, and they might not be nearly as merciful to their defeated rivals as he was. Ironically, Pompey would be pretty well-positioned to be the Caesar substitute (as far as 'kicking the Optimates' teeth in' goes) in this scenario - he was never a doctrinaire Optimate in the vein of say, Cato the Younger, and despite being initially aligned with Sulla he and the Optimates actually became enemies (even without that whole 'First Triumvirate' dealio, Pompey had been racking up way too many successes for their comfort) until Caesar started looming large over both of them.
Pompey also has built-in 'Augustus' replacements (the ones to establish a lasting empire after his death) in the form of his sons, especially Sextus Pompey who seems to have been quite competent in his own conflict with the Second Triumvirate. In turn I'd imagine Crassus, Rome's richest man who was a more consistent Optimate and a rival of Pompey's until Caesar started mediating between the pair, will step up to take Pompey's historical place as the Senate's champion against the Populares.
The Roman Republic was already pretty much a walking corpse after the murders of the Gracchi brothers and Sulla & Marius' violent bout, and removing Caesar does nothing really to alleviate the root causes of its terminal crisis. What Cato and the other Optimate hardliners hoped to achieve basically amounted to trying to revive someone who's already braindead - and there were more ambitious generals than just Caesar lining up to pull the plug on the poor bastard's life support.