They should remove the main story daily altogether, remove all cut scenes, or rework it to show a different recap version at the end. As tank I also hate waiting and when I see a bonus, I ask if they care for the cutscenes or not. If they do, I just leave and make gil crafting or decorate my house for 30m and get a instapop and repeat. Usually by the 2nd queue I get the rush hour anyway.

Hopefully, my exit didn't take others with me since the penalty for them is completely removed at this point and they stayed to help. If not, then just like most dungeons nor trials, they need to form a party and queue up their own version.