No thanks. You still haven't solved any of the other problems that this would cause. The fame is the least important, though most obvious, of them.
While this wasn't my solution, merely an agreement that a game mechanic made sense in an IC way. Perhaps you could catalogue all the other problems that this would cause because I've only read of two being discussed:
1) Fame Whoring
2) "Forcing" another character's unit to kill you
