I'm 100% in favor of a universal DH. I'm 100% against limiting pitching changes.
What I don't understand is why they don't just require zero warmup pitches for a reliever coming out of the bullpen unless he begins the inning. If a guy comes in after an inning has already started, he should be fully warm from his pen throws. That eliminates the issue of pitching changes taking time, while still allowing a manager to use matchups.