Well, that's quite a wall of text. I'll just respond in a more compact form :P
The problem with your arguments on 1, 2 and 3 would be "feeling", which you admitted to it that it's all "personal feeling". I have my doubts whether observing every single player in the DPS seat, looking at their rotation/animation order, doing your own job while watching the field is... feasible. If anything, it's all "paper chemistry". While it's true on paper, it does not (always) apply in practice. Even if it does, it's only true for a very selective individuals who somehow can keep an eye on the animation (order) of 4 players in addition to their own role while also observing and responding to the playing field.
Here's another thing about "personal feeling"; it's not a valid reason to elaborate why someone's performing poorly. You're all for personal parsers, but here's one flaw in it: It doesn't work or make a difference. This leads to two cases:
Case 1 being denial. If no one has access to your numbers, what is preventing you from hiding it?
Case 2 would be drawing conclusions. If your numbers are fine, there's no reason to hide it. If someone would hide it after all, the logical conclusion would be that their numbers are terrible. (let's just go for pure DPS numbers for now, rather than in depth information like skill rotation)
Ergo: Regardless of a parser being public or private, it would hardly make a difference.
There's a possibility of case 3 where multiple players would hide their data. This would actually be the worst as rather than eliminating the weakest link, the entire group is more likely to break apart and unable to achieve the common goal they have gathered for. Even if majority of the group is perfectly capable.
As for your guide, you mentioned you used "math". I think it's safe to assume you've used a program to help you do that. So how exactly would this be different from parsers? Parsers simply simplify it for this sole reason. It does add one benefit. Namely numbers. Numbers are much easier to grasp for the guide's effectiveness, rather than a "theoretical guide". Without the end result (the numbers), how could you prove your guide's better, if not just as effective, as another guide?
There's one particular thing about the whole personal parser or public parser "discussion". This "fear" without base for being alienated because you're doing poorly. But isn't this exactly what parsers should be for? Improving yourself.