Not necessarily. The Free and Libre Open Source Software (FLOSS) movement is a thing. Most of the Fediverse is FLOSS, and I doubt there's anyone who can take Lemmy or Mastodon closed source and buy every instance and then stop pop-up instances. It does require quite a bit of work, though, so it is difficult.
I think the real challenging thing is that a great FLOSS service needs to attract attention and care. When I bring up Fediverse/FLOSS alternatives to software my friends complain about, I'm met with lukewarm-at-best reactions, generally due to networking effects (I think).