Some may recall the round-the-world PanAm flights many years ago, all using one callsign (Clipper 1? I can't recall exactly). At Heathrow we several times had two aircraft active using same callsign!
The only sensible system would be to revert to using aircraft registrations, which are unique and was the norm 40+ years ago, but the stored flightplan system would have to be changed somewhat I guess.