But all quasi-legal systems make it easier to undo wrongful punishment than to retrospectively add punishment and the red card can only be rescinded if the referee says he made a mistake as far as I am aware. Why should foul play be treated differently to other mistakes - should the FA be allowed to add a couple of goals if they were wrongly disallowed?
No. But that does not imply that serious foul play and violent attacks should not be punished. Here is a situation where you can rectify a wrong. Arguments that come down to "Well if you can't correct all mistakes (e.g. wrongly disallowed goals) then you should correct none of them" are totally wrong-headed.
When the FA has the opportunity to enhance and improve the refereeing of the game it should be taken. More common sense, more likelihood that cheating can be dealt with retrospectively will not undermine officiating of games but enhance it.
Won't refs have an easier time of it if players knew that pulling the wool over the ref's eyes by diving or elbowing someone when the ref can't see WILL get caught later on?
If I were a ref I would love to know that there was this mechanism whereby players could be punished retrospectively - less benefit to them in trying to trick me or do stuff I can't see.
The whole "undermining the ref's authority" argument seems to take a rather 19th century idea of authority. Authority should not be mutually exclusive with the ability to correct mistakes - to increase accuracy and improve outcomes.