Data integrity is maintained through FK, unique indexes, proper modeling, etc.

Also, an RMDBS is hard to scale horizontally, so the more CPU tasks you put on it, the sooner you will hit a bottleneck that is not easy to get out of. A application layer, if designed properly can scale a lot more.

>The app will be gone long before the data.

When this ever happens, it happens rarely, and the situation is the data enters a read-only state in my experience and happens during sunsetting. Most of the time, if a new system is required, a migration occurs to a new schema that the new app supports.