I think you COULD but it's true you might end up with one DB connection per API call which might overwhelm your database server if you have too many concurrent

I think you COULD but it's true you might end up with one DB connection per API call which might overwhelm your database server if you have too many concurrent requests that would be better off sharing a connection pool. For such scenarios you'd want more control than what serverless paradigms offer. On the other hand, most admin type API's don't get called very often.