I think you may be misunderstanding the “free” part of FOSS. FOSS - also known as free software - is free as in freedom, not beer (this confusion is also why I refer to it as libre software). It has nothing to do with money - it is all about having control over the software that you use.
Some here have already pointed out the massive proliferation of libre software that forms practically the entire foundation of the Internet, but I would also like to mention that there are some projects that might even say that being libre software has made it more sustainable; for example, here’s a talk about how the GPLv3 (a copyleft libre software license) keeps the Samba project alive.
There are certain monetization approaches that are infeasible with libre software, yes, but I would argue that this is only ever the case with practices that are anti-consumer. Games as a service is a good example of this; I think it’s absurd you can buy a game that you should rightfully own indefinitely, only for it to become literally borked because it was specifically designed to always be connected to the game company’s servers which could be taken down at any moment. With libre software? You have access to the source code, so it’s not impossible anymore to get your own server running if someone else hasn’t already made the necessary modifications to make it happen.
The philosophy of (and reasons to care about) libre software isn’t quite the topic of this post so I won’t elaborate too much on it (unless you want, of course), but feel free to take a look at this page which discusses just that if you’re interested.