> That's fine when one application is using the database.

It's not even fine for a single application. Said application has bugs in it. Said application can (and will) crash in unexpected ways that leave the database in an invalid state. And if you think that "oh, that will never happen to me". You just haven't been around long enough. It will happen, every single time. Any system without foreign keys will have corrupt data in it. Said system will have user-visible issues as a result.

Just like only the backend can truly validate user input from a webform, only the database can validate its input.