Teams don't have to be playing an offside trap to compress, but in the case of a flat back, the flat defenders better work as a unit and not individuals. It does no good for 2 or 3 to step up and one or more to stay behind. A trap is normally run just before a pass forward. On the converse compressing the attack is generally when the ball is not able to be passed forward. All of this can be mandated in practice.
Coaches generally have a tough time getting the players to talk.
The biggest problem, though, may be the players that don't listen. Players don't talk for several reasons. One is lack of confidence and understanding. If they don't know what is going on, then what are they going to talk about. Players won't talk if they feel as if their communication is not being heard and acted upon.