Let me offer my view: if there was no Caesar, then someone else like Pompey would become Despot formally or not. Pompey alas was already kingmaker in the Senate and had a degree of power which influential figures like Scipio Africanus would never dream of or achieve during their time.

... If not we have the examples of the later Octavian-Anthony duumvirate, and prior to them Sulla and Marius. After the Gracchan disorders everyone was only concerned with individual enrichment and power grabbing, and the Senate faded into irrelevance forever. So much that the Republic could not be theoretically restored later lest someone else would wrestle power and become Princeps by the force of arms, an ever present threat.

It is a fact that the Princeps himself could do and say things which the worst Kings of Rome never could without reaching a limit or deposition, so the absence of a formal kingly honour was merely the hypocrisy of the many who long ceased to be fit or willing to have anything else than unbridled Despotism as their deserved head. Rome during the Monarchy had a super-personal reach, as the creation of the Comitia Centuriata and the prior existence of Curiate gatherings show us, but the difference between them and the later Senate is that the Senate was merely a relic, whereas the need for the Comitiae as a moderator and advisory body was real; no representative institutions were created during the Empire, contrarily to the Monarchy.