Its perfectly possible. The game packets are identical in this day and age of code reuse, cross platform developing, abstraction, and lowest common denominator target development.
But each side would rather make you buy it again for their system than do something remotely considered supporting the competition.
The online service shit like XBL and PSN is to blame. They use those services to paywall and vendor lock in.
Give me a join by IP option to play anywhere I want without being pigeon holed into a multiplayer paywall.