AGPL covers users interacting with the software remotely through a computer network which is not the same as covering hosting. There's often overlap but if it really is hosting that a project doesn't want to allow then they need something other than AGPL.
If you want to prohibit hosting then yes you're going to need a non-OSS license (by definition), but that's moving the goalposts: I was replying to a post that said others should be allowed to sell the software as a service, but that they should be forced to share their changes even if they're "hosting" and not "distributing"... AKA the exact point of the AGPL existing.
AGPL's tying that to users remotely interacting with the software over a computer network still leaves a lot of uncertainty about when it applies.
Consider this case. Suppose there is a chess server that users can interact with remotely over a computer network to play chess against other users or against a chess engine.
On the same host that is running the chess server there is a database server, which is only accessible via a Unix domain socket on that host. The chess server uses that database to store game scores, an opening database, and some endgame databases.
The database server is AGPL. Are users of the chess server entitled to the source to any local modifications that have been make to the database server?
Does it depend on whether it was the people running the chess server who modified the AGPL code or of the modified AGPL database was provided by the hosting company?
Most of the incidents I remember where a software developed was unhappy with someone offering a hosted version of their software were cases where the hosted version was mostly being used by clients of the hosting service and being accessed over the hosting services internal network rather than cases were someone was hosting a version of the software to provide that software's services to end users.
