You need some entry point into a peer-to-peer network in order to make connections with peers. This often takes the form of a central server. In theory you can do have it be a bit more decentralized and have an initial list of peers to try to connect to who can then communicate about other peers, but you still need this initial entry point which is a potential point of failure long term, and I don’t think any games actually do this?

So… Technically speaking, in order to reliably connect peers most games are going to rely on a central server, which does technically cost some money to run, though it should be much cheaper to host than a proper game server which will actually be running the game and physics and stuff server side. With older games like quake you could easily connect to a server even without the master server (though you wouldn’t be able to use the server browser) and it was not terribly difficult to replace the master server with an alternative one.