Database-per-tenant is great for read-heavy apps - most tenants are small and their tables don't have a lot of records, so even very complex joins are very fast.
The main problem is that release times can increase substantially, because you have to migrate lots of individual databases one by one, and sometimes schema/data drift can occur between DBs, and then your release stops midway and you have to figure out why in some tenants the feature works, and in some it breaks... So it's not free launch, the complexity just shifts to a different place.