I don't know much about police training but one would think they are trained to not coerce people if they don't have the legal right to do so.
This is untrue. Police officers are trained pretty explicitly to use implicit coercion like you just described (if I don't do what the cop says, I'll get in trouble or hurt) to get people to waive their constitutional rights. (Do you know how fast you were going?) It's a metric-seeking approach for them.
Just the fact that the cops asked for ID in this scenario should make it clear that, in fact, cops ask people to waive their rights all the time.