People need to get with the program. Pick order is no longer a thing in dynamic as far as i'm concerned. 10/10 times, you get your first or second pick for lane. If you can't be happy with one or the other, there is no hope for you. You can still always ask for a trade and there are many willing people, but the person you described is the same as any individual who is lane or feed mentality in old champ select regardless of pick order.
Personally, I take the easier route out and just go with another lane because I don't like conflict. I don't agree that it's the healthy choice, because it just enforces that other players behaviour though. Sometimes, and I think this is the better option, just play the role you were given regardless. Your team may still end up doing well, but be prepared for a loss. They are in the wrong, so if your team loses because of their stubborness, it's going to be on them. If you can't afford that one loss, maybe bend a little but don't do it all the time.