What leads to toxicity isn't the parser (that will exist in the game nonetheless) but the over reliance of the game on DPS.
You 're a healer ? You need to DPS.
You re a tank ? You need to DPS.
Everything is about DPS at endgame. It is the pinnacle of hypocrisy to design the game that way but forbid the use of parsers (yet alone not implementing one in the game). Back in 2.X, where the meta was far less about DPS than it is currently, there wasn't such a commotion about it. However, today, I can understand why people ask for parsers and I don't think any group of serious people about endgame (especially ultimate fights) will actually come and say they don't use parsers or third party website to study what happened during the fight.
Its also what leads to the schism between people who play the game to simply collect a few glamours, run the 24 players raid, 4 men dungeons, etc and people who partake in 8 player content. They simply don't share the same vision. Because in one part of the game you need to push for DPS, while in the other the game tells you its ok not to be very good at it. And it is what is transcribed here : some people don't see the point of parsers because they don't need it on the content they run, while some ask for it because it is needed in one part of the game.