This is all great information, and I agree that you don't need parsers to see who is doing bad.
A lot of of us would like some kind of personal DPS meter because we are good, and we want to be great. What is so hard to understand about this? I play on PS4, I don't have the option to run a 3rd party parse. I feel like my rotation is solid, and I'm always hovering around top-2nd DPS on enmity, but how am I supposed to learn that I can squeeze another 5-10 DPS out of what I'm doing? I mean, how am I supposed to know it's even possible? Just take someone else's word for it? And then normally what you get with your PUG instance, is someone telling you how to do your rotation for you to examine their profile and they haven't even touched the class yet, let alone have the job.
Also, how does your instance solve the problem if the "leader" of this static in your example is the one who has the rotational issues, but won't admit it? Maybe the leader doesn't like to be told he is wrong? Maybe he doesn't respond well to criticism and it causes a rift in your static which throws a wrench into gained chemistry? Since we are dealing in hypotheticals here anyway.
Many of your examples you gave are quite easy to see in plain combat. You don't need parsers or tools to see if your DRG isn't keeping up HT or if you BRD is singing at appropriate times or not. These things all have visible buff/debuff icons for you to look at. It would be nice to have something more visible, for those of us who know our rotations but want to experiment on pushing the DPS to its limits. And I shouldn't have to ask anyone for help on that!!!! I can't stress that enough. I want to figure it out for myself, not have my hand held through the process.
This has all basically come down to "people not wanting to be judged by their DPS #". Stop deviating from the topic at hand. People do/will try to do bad and ignorant things with any type of anything we are given. That doesn't mean we shouldn't have it. You don't have to divulge your DPS to anyone. The instance given in the OP would be for personal use only. You can always avoid groups that demand the information.