Maybe someone can explain better but with the late checks you are talking about, I feel like whenever a team went in motion or shifted against us we always scramble and have a tough time communicating.
Simplifying could mean a lot of things. Playing more man, or having simpler checks should make things easier. It will be less things for these players to remember when teams show different formations and motions.
Like the 360 guys said simpler=play faster and hopefully lead to more big plays.