I've never understood people who make other party members skip their cutscenes unless it's necessary (moogle fight and speed runs). Really, you can't wait the two minutes it takes to make the experience more enjoyable for them?

Anyway, the main problem in the cutscenes is that the timers don't stop for them and this should be changed. In my opinion, they should just make everyone watch the CS for the first time too. And unless someone in the party skips the CS, they shouldn't take your fighting time.