Been there, done that, didn't regret a thing since i'm certain i'd have given up way earlier (assuming i'd ever bother starting) if i had to use an existing engine :-P.
(ok, i never had money to "make a game company", the most money i ever had was to be able to spend ~2 years living frugally while making my own stuff, but it is close enough since i think someone could say i should have used some existing engine instead - which is true, except i'd hate doing that)
There are people who want to make games, people who want to make engines and, perhaps a minority, people who want to make games and engines :-P.
(though FWIW in my case i never felt the tech side was much of a limitation, it is art/content that ends up being the bottleneck and makes everything crawl down and the stuff i like to do aren't the kind of stuff you could do with procgen, minimalistic styles or other similar approaches for saving on the art/content side)