I'd flip this slightly. The tool isn't the problem, it's hiring and code review discipline. I've seen juniors produce worse code without AI too, just slower.
What actually matters: did you pair them on the auth flow? Did someone review before it hit production? That's on your processes, not Cursor.
That said, you're right about one thing. AI excels at "locally correct" code. It'll generate working Lambda handlers that'll murder your cold starts or DynamoDB queries that scan when they should query. You need people who understand the trade-offs your stack demands. No amount of tooling fixes that gap.