Honestly I dont have a clear solution to that either. Im not against talking with your team about performance if you keep wiping nor am I trying to ignore dps checks wipes can happen to party finder folks. But thats the thing though, dps meters has such a terrible toxic stigma to them in the MMO community that 9 times out of 10 if you try to explain the mathematics behind their performance that just leads to arguments between both sides and it just becomes toxic. I speak of this from experience and hearing stories of many groups in other games whom just take the numbers waaay too seriously and use it to measure worth of players, its just part of the ugly side of human nature in online game, and its a variable the devs can at least prevent from just not openly supporting the tool into the game.And as noted, I really don't think just building a DPS meter into the game is a solution to either of those scenarios, for a whole variety of reasons; I think the former one can be solved with some creative design (witness the Google Doc I linked... lord, I don't know, many pages ago), though the second one seems more thorny. But I do agree with others that there's some value in maybe examining those two scenarios.
Personally most of the conflicts I run into are due to people failing mechanics more so than dps, Ive rarely ever run across party wipes where we didnt clear a phase due to everyone not perfectly maximizing dps performance; even with everyone alive, no rez debuffs and we used our LBs. Im not gonna say that your given situation doesnt happen though. The most you can do if you want to talk to random strangers in a party about improving performance is going over their rotations. You shouldnt expect other players to play perfect dps numbers in content, you should expect them to at least understand their job's toolkit and how to use their skills properly.
And yes if that means you keep getting multiple wipes from a dps check, then that just means that you and everyone else arent fully capable of clearing the enrage. If my group keeps wiping in the same exact phase with the same exact makeup (everyone is alive, LB3 usage etc) then I dont need dps meters to understand that we arent clearing the fight because our group cant deal enough damage; either maturally address this to them and if not just bail. I dont hold people against quietly bailing. For the most part if I see obvious human error during wipes then I give them the benefit of the doubt and try again.