The problem is not the rhymes as such being overused, it is the cliché thoughts that tend to come with them. If your song has a new and original message well told, the rhymes are likely to sound equally fresh.

There are in fact rhymes (such as the "Coriolanus" above, which of course I love) that are funny or clever in themselves, and which like all other sorts of joke or witticism can be told to the world only once.