This is a weird one. I can understand why they use “flight number” rather than the individual aircraft’s “tail number” ... And sort of understand why the same flight number in both directions, although that makes less sense.
Wouldn’t AA1234 in one direction and AA1235 in the other make more sense? That would seem to uniquely define each flight.
Or maybe it just isn’t a real problem?
You raise an interesting point. The tail number seems to be a good idea.
General aviation has used “tail number” which are FAA-issued N-number callsigns and no two are alike. This is just a company-issued flight number made up by the airline.
Flew recently on a JetBlue flight, they did exactly as you suggested.
I ALWAYS THOUGHT FLIGHTS WERE NUMBERED DIFFERENTLY