Can't a ref just say also check for any foul play?
The issue is that the bunker shouldn't have to because for 'foul play that warrants a straight red' (technically head contact is also foul play) it's either a red or nothing. There is no in between. For head contact there are varying degrees of offence that could be a YC or could be a RC.
The bunker is supposed to save time for head contact where there are lots things to consider, such as impact, amount of force, any mitigation etc... and it wastes time for the ref to do it live.
Say a player punched another player the ref wouldn't say, it meets the YC threshold, I'll send it to the bunker. It would be a clear red and sent off straight away.
WRU probably didn't anticipate that a ref would send a situation where a player has headbutted another player to the bunker because in reality it should just have been a straight red. The mistake was completely Carley's and the bunker was asked to review something it shouldn't have. Why make the game more complicated by asking the bunker to also review if something is worthy of an automatic red.
Let's take for example the incident where Ben Thomas was asked of eye gouging. The ref looked at it live and determined it wasn't an illegal act, just a bit careless with his hands and fingers. Now if the ref had the option to send him to the bunker, he could well have just said I'll yellow card. However, if the bunker says it's not foul play then Wales have lost a player when they shouldn't have.