> I can't think of many apps that don't require custom logic between receiving an API request and persisting something to the database.

I do. Most apps we write (government stuff) are CRUD apps that mostly handle data from the user, and then apply some logic to that data.

You can write custom logic in stored procs no problem. It's even a lot faster than doing it in java/php/ruby/.net or whatever because there are a lot less layers between you and the data, and the procedural language you use inside the the db is explicitly made and optimized for this purpose.