I've noticed that most of the time we don't push or we push but then don't start to taxi until the safety demo is complete.

On a mainline flight today we were well under way.before the demo finished (tbh, I only noticed because we were crossing a runway and trying to figure out if it was our departure runway or just a crossing)

I know there are some elements of the demo that 14 CFR requires are completed before milestones (before movement/before operating above 10k feet, etc.) but is there a reason or guidance to wait out the entire demo before doing anything?