Star Wars the Old Republic despite being an MMO had a pretty good way to keep parties of players engaged during cutscenes. Everyone got to pick their preferred dialogue option (or pass) and the highest roll wins. BG3 having a similar system would be lovely as you could have chances to change the course of a conversation which gives more incentive to stay involved in the convo to begin with. Also would give the option for characters with poor social skills to keep their mouth shut if they want to rely on the charismatic one to handle it. Also gives fun chances for the idiot barbarian to steamroll the nerds who are trying to hash things out peacefully and just force a fight instead.
It would also be nice if some of the checks were more complicated than PASS - good thing happens/fight avoided VS FAIL - FIGHT.
like what if you were 1 off? maybe they are now on edge but the conversation can continue? or what if you only just succeeded? they are a bit less wary but not ready to just give you what you want? I guess some DMs might run campaign with checks being as simple as pass/fail but I think most of the time there were degrees of failure/success. Others have also mentioned that it can be really fun to have the consequences being more varied as you could actually have more interesting things happen on a failed check in some instances.