This is what mastodon.social is doing now. Making it so people don’t have to think about the instance at sign up.

TBH, I don't find that all too bad. As long as users can easily move at any time, getting them set up on a popular one first where everything "just works", they can learn the concepts and get used to the federation stuff. Then after some time, they may realize that a smaller server might fit them better and can then move there. Choosing a server without ever being registered somewhere (in the fediverse) was even hard for me.