I considered this, as there is a lot of between-round AP from players as they have to plan their whole turn from scratch. I thought being able to forward plan a little would speed up the decision making.
However, I concluded that certain assignment tiles being permanently assigned to certain colours of dice would make those dice, and by association those helper actions, considerably more lucrative. I don't think the game would be as fun if everyone was fighting for the exact same colour of die every round. Strategies would vary significantly less between players.
I can see that possibility. You would probably still feel the same if the Private Messages variant was used in conjunction with this idea?