Many older fans believe the final should be held at the home of the champions as that's how it used to be. However it has now been held at Wembley (or other neutral venues) on more occasions than at the champion's ground.
Arsenal didn't play when they won the double in 1971 and in 1972 and 1973 City played in the game even though we didn't win anything. The FA moved the game to Wembley to generate more interest at a time when Wembley visits were rare in the hope that the champions and cup winners would agree to take part.
The decision to play FA Cup semis at Wembley has reduced the rarity value considerably.