I think it really depends. If you have a big number of simple queries (easily resolvable by table keys) for not so relevant data (daily backup suffices), you might want to avoid the delays caused by network latency and stick with the local db. Security is another issue. If you need security and can't secure the network between host and db, you will start thinking of encrypted links; expensive and slow. And last, another network component is another degree of complexity and potential source of failure.

There will be good reasons to use external db hosts, but it needs thorough thinking. Anyway, I agree absolutely that a good admin must consider the options.