"Prison Break" question

Seems as if it would make good sense, after breaking out of prison, to change one's looks...and I'm not just suggesting putting on a baseball hat. If I had hair, I shave it. If I were clean shaven, I'd quickly grow a beard, etc. But noooo...not on television. That'd make it too difficult to identify escapees in a nanosecond or less. Just sayin' ...