Yes, it would work fine if all our users were perfect. Let's continue with the same example and imagine what Catgory:Finland would become like. 10.000 images, maybe? Then we have this dufus (see http://commons.wikimedia.org/wiki/Commons:Welcome_log) who uploads an image with only [[Category:Finland]]. That image will be lost forever. No one will ever find it and no one will ever be able to use.
One could create a query or a special page that lists images with few categories. Maybe we could even sort them by age ...
We could. The problem is that it would make a common user more dependent on the work that admins do. And admins don't need any more jobs - we can't handle what we have now. But that is not my main concern. Maybe, eventually, we will cope better with the workload.
My main concern is now, if we have a problem that needs fixing? Or if we are inventing one because we have a technical way of solving it? (With an external tool whose interface was so difficult it took me ten minutes to figure it out.)