This doesn't work because DBAs are rarely on the dev team's sprint schedule. If the DBAs are blocking them devs can and will figure out how to route around the gatekeepers. In general, keep the logic in the app not the db.
We have sprints. We also have super responsive DBAs. Keeping the logic in the app is the path to unresponsive database calls. Been there, done that. Not going back to that crap.
In all seriousness, I won't work for an organization that works the way you describe. It's a red flag and a sign of organizational issues, personality issues, and ineffective management. Don't need to waste my time at a place like that.