Well, it all depends on the ambitions and the roadmap of the project. It seems to me that if the first listing of a company takes place on a small exchange, but they point out and work on listing on a large one, this can give good results. Even now, it is not uncommon for a coin / token to fly up tens of percent after listing on a new large exchange. But at the same time, it must be borne in mind that the chances of screwing up are just as high.

I agree.
There are projects that are just pending with bigger exchanges and got accepted the listing for smaller ones and that's a good start for them. But, there are those projects that don't really want to get into bigger and popular exchanges.
Because that's all they want, to stay on that small exchange and waiting for their project to die once they're all set and done profiting with their project.