If running a parser makes you cynical and depressed, why do it?

[Vidu]

You're packing a lot of things into this, so to adress them one by one. I do want to preface this however by saying that while there is nothing wrong with enjoying the game "blindly" and in a very relaxed sort of way (I think of it as how my mom travels: "Oh, we dont need to worry about catching our train, if we dont, we'll just take the next one!") some people also enjoy the level of performance you can achieve in this game and theres nothing wrong with that either.
To adress your points seperatly now, though:

1) Tank DPS: As a tank main I personally never cared to much about it, but I can see why other people do: They're setting themself to a high(er) standard and their reward for that, aka seeing their effort being reflected in a better dps-output. Now I dont know the exact numbers that I read somewhere recently but apparently Tank-dps got stealth-nerfed with Shadowbringers, which means that people who are putting the same amount of effort in as before are now getting less of a reward. I can see why that would piss people off - but at the same time those people still want to know if they're doing at least aswell as the game currently allows them to, so they keep looking at numbers.

2) Other peoples dps: This is super simple, actually. At least to me it is - because to me its super annoying and feels almost disrespectful when I go into a duty, try my best, push my dps as much as I can and try to achieve perfection only to have all my efforts destroyed by this little dreamer whos only using half their toolkit in a level 80 dungeon and is therefor dealing less damage than the tank. Its just frustrating to know that this 25minute run could have been 15 had that guy at least tried a little bit - of course dungeons arent a race and I get that some people just want to enjoy them at a slower pace, but this is this "reward"-situation again.
And why look at numbers here? Mainly to ensure yourself that its actually not you whos holding back the group.

3) DPS jobs who arent dealing enough damage: Specially those jobs need to look at their number to make sure they're making the most of what little they have.
In regards to thinking that certain jobs are "ruined": To discover jobs being unbalanced its actually important to look at numbers, the devs do so aswell. If a job cant perform well enough in a raid-setting (not enough damage output and/or utilty) you wont find a group when playing this job - so yeah... that job is "ruined" but with reason and it can be fixed.

You also need to keep in mind that complaining about something doesnt mean you dont enjoy it - infact it might show that you're really passionate about the game. People who complain care about something. People who are upset about changes to their favorite job care about that job - your approach seems to be more on the lines of "so what" and from my perspective thats a terrible stance to take. Because it shouldnt be "so what" if someone cant play their favorite job anymore because groups dont want to take that job with them or because they themself dont feel useful enough to a group.
The same goes for being upset about other peoples DPS: Its because people care about performance - both theirs and their teammates - instead of just being indifferent to it.

And at the end of the day, wether or not you look at the numbers or not: They matter. A boss doesnt just drop dead after being hit a random amount of times or after 10 minutes have ellapsed.

I dont think its seeing numbers thats turning people bitter and cynical - I think its seeing their efforts invalidated by the game itself (job balance) or others (poor performance) thats draining the fun out of the game - and honestly: You dont need a parser for that. I dont need a parser to be annoyed that this RDM didnt cast a single AoE-spell during this expert-roulette and didnt had proper gear on (because I can see both just fine without one). And I dont need a parser to be upset with myself for missing out on some Confiteors (because I know I missed out on them and even why).