So in other words parser toxicity is the most common form of toxicity in WoW that you know of, given you can't even remember anything else.
Firstly it's very unlikely that's the only reason why its banned. Another but less mentioned criticism about parsers is that players often use them as the sole indication of a class's worth. While this may look harmless at a glance, this is something that actually threatens class identity.
It's well known among raiders that certain classes have lower dps potential to balance out having utility. Proper raiders usually understand this balance but outside of that playerbase it tends to be misunderstood. Some people automatically assume a certain class isn't worth playing if the damage output of another is higher, and they don't even give a thought to utility. As time went on in WoW utility became less and less relevant partially because the community began to prioritise damage far above everything else. This actually caused a lot of friction because players felt like their favoured classes/specs were being overlooked, and it was a major contributing factor to a lot of class homogenisation. If there was an official parser I'd be shocked if rdm would still be as popular as it is now. Right now it's mostly the raiding community who hesitate to take rdm on anything but progress. But if everyone could easily see how much lower their damage potential is than a smn, rdm would be significantly less popular even outside of raiding circles.
Secondly this beneficial tool is too easily abused, and thus it can become the opposite of a beneficial tool. I won't argue that it's beneficial to see your performance in a way that can be analysed, because it is. However the issue is quite a large amount of players don't know how to use this tool properly.
In WoW I got hassle on an alt because my dps was crap...but it was crap because most of my dps came from dots and mobs died well before they could have their full effect. I tried explaining this but all I got was "lol l2p". The funny thing is on my main I played the same class and I had among the highest dps in our raids even though it wasn't even my main spec. I definitely knew how to play it. But due to classes not being designed to be balanced in low lvl content, and encountering players who don't understand this, I got hassle over something completely out of my control. This was far from the first time I had seen something like this happen.
I already see this sort of thing in XIV. Every so often when I pug dungeons I see healers given snarky remarks over lack of dps even though the tank is obviously putting them in a position in which they can't do much dps or else there will be a wipe. This is already happening just from people watching hardcasts in the party ui. Can you imagine what that would be like if everyone had a parser?
No I'm not, I'm blaming people who don't know how to use a parser correctly and people who intentionally misuse it. I think parsers are great tools, but I'm also painfully aware of how common it is for people to use them incorrectly. I don't think any amount of tutorials or in-game help messages would mitigate that. Parser misuse is still happening in WoW despite the fact it's been in the game for over a decade. If a lot of the community there still can't use it correctly after all this time, what makes you think XIV would be any better or different?
All this being said I think XIV should give better tools to allow players to access their own performance. At the very least the game should display personal dps. The stone sky sea dummies should also display dps instead of just giving players a timer to go on and forcing them to go to a third party tool to glean the true meaning behind their kill time. Additionally there should be more analytical utility given to target dummy furnishings, because right now their function is too basic. Currently pc players are at a distinct advantage when it comes to analysing personal dps and I think SE should address this in some manner.
But introducing a normal parser in which you can compare yourself to others at a glance? No I'm strongly against this because my time in WoW showed me the long-term ill effects from it. The gain doesn't outweigh the negative aspects.