When Augustus decided to proscript his enemies instead of showing clemency as Caesar did, he was actively trying to implement changes to Caesar’s way of doing politics that he saw as necessary to unify a republican form of government under his rule. That’s also the reason he decided to attach official powers to himself, and avoided keeping the actual offices themselves for extended periods of time as Caesar did; he had most of the power of a consul, but not the (to his enemies) threatening title.

However, I do not think later emperors we’re looking back at Caesar’s failure any more so than they were looking back at Augustus’ success. The entire history of the early to mid empire could be seen as a series of attempts to recreate and modify what Augustus had started around 30 BCE, and not what Caesar had done over a decade prior. Augustus was the one who ruled effectively for decades, and people looked to his example for guidance. In his Res Gestae, Augustus openly admits that he meant for his rule to be a sort of “guidebook” on how to lead the “republic” as it stood then. The later Julio-Claudians looked to him as an example, much like he looked to Caesar. Caligula, in Aloys Winterling’s argument, wasn’t a madman at all; he was trying to play the game Augustus played his own way, by acting completely unpredictably and even belittling deliberately the members of the Senate to assert his dominance. He would have been looking back to Augustus’ example for that and implementing changes that worked for him. Tiberius, too, could be seen as another example of a failed attempt to recreate Augustus’ leadership style; it is clear in Tacitus and in Suetonius that Tiberius was unsuited to fill an “Augustus” role in the new government (which was poorly defined and in which he was inexperienced when he rose to the throne, as it were), and he paid the price for his lack of skill by being manipulated by those around him, eventually forced into early retirement at Sperlonga (this is Champlin’s idea).

To answer your question more directly, I think Caesar’s failed clemency is more an indirect cause of the brutality of later rulers, being interpreted through how Augustus changed the game during his rule. It became clear that the only way to lord it over the proud senators was to control them through force, and that’s exactly what some of the more successful Julio-Claudian emperors did, until it became clear that the government was no longer a republic and was in fact an empire.