An important caveat: an exfiltration vector is not necessary to cause show-stopping disruptions, c.f. https://xkcd.com/327/

Even then, at least in the Bobby Tables scenario the disruption is immediately obvious. The solution is also straightforward, restore from backup (everyone has them, don't they?) Much, much worse is a prompt injection attack that introduces subtle, unnoticeable errors in the data over an extended period of time.

At a minimum all inputs that lead to any data mutation need to be logged pretty much indefinitely, so that it's at least in the realm of possibility to backtrack and fix once such an attack is detected. But even then you could imagine multiple compounding transactions on that corrupted data spreading through the rest of the database. I cannot picture how such data corruption could feasibly be recovered from.

Right, just because someone can't sneak out usernames and passwords doesn't mean they can't cause inaccurate results in their favor, like a glowing recommendation for a big bank loan.