These are the rules that have their roots in protectionism of the markets. It wouldn't be fair from EASA to dump this rule, allowing influx of other pilots on European market, when somebody with EASA licence has to go through the same process if he wants to fly N-reg aircraft.
Don't remember that licence itself is not enough. And vast majority of EASA licence holders also hold an EU passport. Same goes for FAA licence holders - most of them are US nationals.
Don't see airlines parking aircraft because of this. It has been like this since forever and it most likely won't change.