Well yes it can be useful to move it at times.
Maybe your original cap was off in a corner and corruption at the other end is killing new cities.This would be mainly for Monarchy or Republic.
Or maybe you want to relocate to a better defensive location.
or if you launch a ship and build a new palace in size 1 city with 1 defender and no walls,if you lose that city it is destroyed but your spaceship is not.Capitol must be captured to destroy spaceship.
maybe in MP,if agreed upon ahead of time,you may want to share a wonder by swapping cities.You can't gift or trade your cap.So you would need to move if there was a wonder there you wanted to share.