Well, Booster grew up poor, didn't he? Even in the future, I bet poor neighborhoods have rat infestations...and I bet future rats still carry all sorts of nasty diseases.

Playing on Piper's sympathetic nature would probably work; he is generally a nice guy, and would try to put away his rat obsession. It's not like he had it *before* he was sent to Iron Heights, so it's not intrinsic to his character. It just looks really cool, in a freaky rat-covered way.