Playing the devil's advocate: then you still need somewhere that people can get the current repository state from. This place might not need to do anything with pull requests or any other write action on the repository, but somewhere to clone from is necessary. This would then be the "hosted" repo, and the patches sent via mail are just that, patches.
Sounds like you're talking around semantics. Yes, any server you connect to as a client to clone a repo is "hosting" that repo. But that can be practically any computer it doesn't need to be a _dedicated_ host in a server farm, it could be a devs laptop.
Fair enough, but there is still a hosted solution, it's just hosted email instead :) I know Linux used that approach, which is seemingly ironic since Linus made git, and previously used BitKeeper. There seemed to be some problem that emailing patches to a mailing list wasn't solving to motivate the invention of git.