Did Caesar even have children, and if not was it ever explained why he didn't sire an heir? In the years he conquered the tribes, you are telling me he never fucked the chief's daughters? Sure, there is no guarantee that the son will be as good as the father, but that is one way of continuing the cult of personality, hell you could even secretly send him to the same University, Caesar went to, to get an actual education, and that could make for some interesting stories, maybe he is one of the smartest students in the University, but he is extremely violent and the professors keep debating if it's worth keeping him around or not, or maybe he fully denounces Caesar's ways, and embraces the NCR, until he realizes how corrupt they are, and goes back to Caesar. Knowing how to kill people, is not enough to run a state, you need proper management skills, as well as properly choosing the best people for the job, like who is responsible for the roads, or food distribution.
Personally my biggest problem with Caesar is that he is an unironic globo-homo, he conquers a tribe, and then mixes them with all the other tribes, to destroy any sense of individuality, culture or history, just to create Legionnaire mutts. He is the kind of person, who would unironically want to mix up all the European nations as well as to add a mixture of African and Muslims, to create perfectly loyal European mutts.The NCR is bad for different reasons, but at least they let people keep their individuality and culture, and someone can say that they Boneyard descendant and that he is different from other people from NCR territories.
Let's say he actually conquers New Vegas, and that becomes his new Rome, what culture can he even produce? What schools will they even have? Who would even go there to teach? Are they going to kidnap teachers from the NCR territories? Send a few dozens to NCR universities, and then hope that in 5 years they come back, still loyal to you, and start recreating NCR technology, kinda what the Japs, Chinks did in the UK and America? Also he will have his capital at the far extreme of his empire, how well could he even manage the far eastern territories from Vegas?