There are few cutscenes when a party is waiting for you in a dungeon past things like Prae or ARR that are heavily story focused. That said, even if it's just the cutscene introducing the boss, don't skip the cutscenes. We understand, or we should, that when we use a random matching system to create our parties, we may have new people in the party. And if vets are too impatient to wait, that's on them. Enjoy your cutscenes.

Also, come ShB you can run MSQ dungeons with NPCs in the Trust system. So you won't have that pressure to skip any longer if you use those.

I'm personally of the opinion the forced grouping idea of the MSQ does more harm than good. Trusts were a good start there, but the main storyline should be designed in a way that it doesn't force grouping or has duties that scale to number of participants. Then duos and trios are an option without having to fill in with a random. Or expand the Trust system so NPCs fill in for the missing numbers. I love how story-focused the game is and I think it runs counter to that design to have even the possibility that someone else would pressure a player to skip the story because they want to finish the run.