All true, but of course you're missing the player agency component that renders those issues moot. If any of the above happens, you can simply find another server.
Private games (now called "custom lobbies") were available back then too, they're not equivalent to a public server browser.
They are functionally equivalent for the player. The problem with player hosted servers is that it was very hard to get a fair and balanced competitive match, where now it's extremely common with matchmaking on servers hosted by the game company.