we've been doing this for 20k databases with mysql for the last 10+ years. It solves more problems than it creates.
Migrations are trickier, but you get sharding, data isolation and easier backups that way.
I'm not saying it's always a bad idea, you just need to think about what you're doing. This was closer to 15 years ago now. We had to develop a bunch of our own tooling, and make our own modifications to frameworks that are now ancient history.
