It's weird how the term "Challenge Cup" permeates sport, because none of the ones using that name are true challenge cups.
The only genuine ones that I can think of are The America's Cup and The Boat Race.
The rules for a challenge cup are that the holder must defend it against the challenge, and that all other competitors may use whatever method they decide upon to produce the challenger. In other words the holder gets an automatic bye to the final.
I believe that the earliest F A Cup followed the rule, with The Wanderers in 1873 defending their 1872 victory.