I'm interested in knowing how common or uncommon is this practice ("server" here means “remote computer that you rent”; hetzner is an example of a company where you can get one)

Companies that rent hardware are omnipresent. But how often individuals are renting servers “for themselves”? Line between ‘companies’ and ‘indie game developers’ is murky, but I hope you get the idea: no higher-up told you to rent a server; you decided that yourself, and now you use it.

I thought that the answer should be “pretty often”. For amateur game developers aspiring to build anything networked that should be obligatory (to test and demo multiplayer, etc). But for the rest, there are benefits too. You can run any computations, store any data, run your game's server-side, demo the app you build. It lets you show whatever you want to show the world.

It's relatively easy to configure and administer a machine (at least, for programmers and tech-savvy people), and providers commonly offer pre-built solutions.

That's cheap (remote hardware gives more bang for the buck). Even the crappiest machines are capable of storing backups and running nightly renders. Want to do some tasks (3D render) faster? Then "rent for an hour" a powerful metal, do your work, and return it (it's manageable but a bit non-trivial)

For me, it looks like if a developer creates something as a hobby, and that something is supposed to interact with other people (=not just games, but any site or app), then a personal remote server is a “must-have” for this developer.

I know a few data scientists that do own a personal server and one ‘digital artist’, yet zero game developers. I don't know many - maybe it's just me. Or, maybe the barrier to managing a server is high? Are "costs too high", or "benefits too low"?