If they wanted to talk they wouldn't play fucking video games.
No. If they didn't want to talk, the should play solo. There is no point sticking the game in the way of player communication. The dialogue should give both characters the option to concede, it might keep the persuasion options too but they aren't necessary - language is wonderfully broad communication channel allowing for expressing far more reasons and ideas than canned dialogue options.
Also, what are they going to do when thre'll reach impasse? Sure, you can wrestle the controller from someone, but what if the game is player online?
They can engage in a cycle of mutual butthurt until they learn to behave like fucking adults? It's called cooperative mode for a fucking reason, even chimps can learn that and they are generally retarded sociopaths by our standards.
I mean if players communicate and agree on some option they don't have to play RPS.
They may still come from different directions (personally or due to roleplaying different characters) and fail to reconcile during standard dialogue exchange. Sticking a retarded unrelated minigame in their face that has to be completed until gameplay proper can be resumed is just bad.
The dialogue could function differently depending on the circumstances (ideally you could even have an option of players starting to work against one another when trying to resolve quest) but generally telling players to make up their minds if they can't agree is reasonable.
Case in point - there are some dialogues in the game already that work in this exact manner - for example recruiting Jahann.
It's shitty all around. If you want a persuasion minigame make a proper persuasion minigame.
I consider it as a skill check with a weird presentation more than a minigame (the purpose was probably to present this as an important feature). I can go with that (of course, it's uselessy long).
The problem is that this weird presentation gets in the way of normal gameplay. I didn't buy Rock Paper Scissors: Divinity Edition, I bought Divinity: Original Sin and that's presumably what I want to be playing after I explicitly chose to install and launch it.
Maybe if the minigame was an actual contest of skill and/or thematically tied to the act of persuasion it wouldn't be as grating, but as it is there is a single irredeemably awful thing in the entire game and it's going to stay this way because part of the audience apparently can't breath and think at the same time.
An option to toss a coin could be there for those desperately wanting game's arbitration.
