If that happened at Essex v Kent, I dread to think what ensued when Men of Kent played Kentish Men!
But in fact that does give a hint as to why cricket is organised on county lines; "local teams often adopted county names." Speculating wildly, could it be that cricket, requiring larger playing fields than football etc, was more likely to be played in villages and small towns, but would attract spectators (perhaps also players) from wider afield, so in the fans' minds the allegiance was more to a county than a town?