But wouldn't using a connection pool solve this problem of "stressing out the database"? I assumed a single connection from the pool would be considered "occupied" until we hear back from the database.

Or are you saying that processing lots of requests/tasks in Rails while waiting for the database would quickly eat up all the CPU? It seems like a good thing - "resource utilization" = servers should do things whenever possible rather than just waiting. Although now that I think about it you'd only want maximum resource utilization if your database is on a separate server.