Not that it makes sense, but I think the reason they don't is that VAR can't get involved with yellow cards, same way they don't get involved for a second yellow.
Tbh I think a yellow for a dive isn't enough punishment, it's blatant cheating and if successful steals you an almost certain goal. I would rather they sack off yellows in the game for diving (never get given anyway) and implement a system where games are reviewed after the fact, and anyone caught diving (including throwing themself on the floor because they felt a slight contact) should be given an immediate 1 game suspension, rising to 2 and so on for subsequent offenses in the season. Would quickly put an end to players trying to con themself a pen as the risk vs reward is much harsher, currently they only risk an outside chance of a yellow card.
The reason I suggest doing it after the game is there's no time limit to it and it stops VAR interfering for 10 mins while they decide if a player dived or not, I'm of the opinion that in the game VAR should have a 30 second maximum interruption, no lines and no slow-mo, maybe a freeze frame for offside. If you can't tell somethings wrong from a quick normal speed replay or a freeze frame with no lines then it's not worth the interference.