I guess it comes from a time when:
a) the FA Cup was seen as the premier competition
and
b) teams could bring in players up to the end of March and so, if they were having a good run, they could bring in new players (short-term loans?) just for the cup.
With all the rules around squad registration and tighter transfer windows, plus the massively increased use of loans, it was probably time for that rule to be reviewed and, thankfully, they have.