Ok, I'll give my perspective as a referee. First some basic background. The role of the referee is not to hand out cards for every offence that a card could be awarded for. The role of the ref is to manage and control the game. If the game is going well and in an "orderly fashion" there is no need to flash cards, even if the foul itself could warrant a card.
This is why I think it's the on-field ref that should make every decision of those kind of situations, as he is the one that feels the mood of the game. If it's a straight punch or obvious kick, then yes, it's a red card, as that is considered putting a bad reputation on the sport.
But the situation with Son was not like that. The ref was in control of the game, and the situation was not serious, or fueling the intensity of the game. That's why I think he didn't send off Son. As per say its a red, but I think the ref thought that the game was not out of control, so he didn't show a red card, because he was well placed to see it. I strongly disagree with the way its done in the PL. I think the ref should at least be the one that has the final say, and that he at least should go and check it himself, to see if there is something he's clearly missed.
I don't think he'd change his mind if he did, because of what I've previously written.