Well there's trade-offs with this too, whether needing aggregate data across shards for features, reporting, etc. Shared data between customers, users, etc. API access, etc.
Sure there are trade offs. If a significant part of the value of the app rely on data sharing or transactions between customers this is clearly unfeasible. But if the app mostly deals with a significant amount of private data of the customers that occasionally needs to be shared, I think using separate databases (not servers) is the safest option.