It wouldn't, so long as it's not merely personally based. Suspicion invites far more assertion than actual, ubiquitous knowledge. When everyone both knows who's underperforming and know that the underperformer knows it, there becomes no more than to comment on directly than one would the color of a whitewashed wall.
Instead, the question shifts to readiness, either technique or effort/wellness -- a difference in knowledge or priority/state. Of any communication that can occur between a party that needs or at least desires change from a given player, that is solely the part that allows for constructive criticism. The effect of universal, full-breadth parsers is to accelerate processes of communication past the majority of less useful and high-toxicity segments and straight to what's useful and for which toxicity, if any, is never purely so.
Perhaps a group will still take issue with a player for coming in without the readiness required by the party, given its description. Perhaps their effort or technique shows clear, almost invasive negligence on their part. These conflicts will still occur, but I do not find them to be toxic, even if they may feel as such to the player being rejected, just as that player's behavior will have seemed toxic and warranting removal to the rest.
But leave it personal, and it becomes a test of suspicion. Consider: you know your own performance, and it seems sufficient, and yet the party is failing. You know it's not you, so it must be one of them. And so, having exhausted, or nearly so, your own limits of contribution, you can only look out for mistakes on the others' part to suggest corrections or party member replacements, if necessary. Your focus is ambiguous and misdirected, and for what... To protect whoever is need of correction from accurate, proportionate efforts of suggestion? And what can you do but look? Ask them? They are free to lie: that is the sole functional purpose of personal parsers. Whatever the purpose, that is the distinction in functionality. One, when underperforming, can avoid responsibility and improvement by lying.
Every distinction between personal and full parsers is one which allows for--even invites--conflict and toxicity. Information is not inherently toxic. Responsibility is not inherently toxic. To ask for personal over full parsers is like saying that people should be barred from their glasses in seeing, and from relevant conversation with, whom they would date. Sure, it may begin more parties/dates, but you'd only have greater and more numerous feelings of disappointment or rejection in the result.
Real-time by-fight performance has far less ability to be used offensively or in grievance than what we already have in the form of fflogs, whereby one's parses can be posted without knowledge to be held representative of your overall performance. That is something actually worth being worried over. It is a place where one would expect to see either only one's best and wholly voluntary reports, or their personally made and representative portfolio of many, many parses -- formed to weigh them against each other and others', be linked for help and suggestions, etc -- and yet singular, outlier parses can be submitted without one's permission, to be held with no distinction to fidelity whenever one's name is searched. That allows for unfair discrimination -- a sense that one's perception is out of one's hands. That is problematic. But a real-time check of one's performance in a given fight does not belie one's performance in that fight. It's just pure information that does not pretend to any context or implication greater than itself.
Edit:
To be clear, I'm not saying that even just a personal official parser wouldn't be a massive improvement, provided it can render at least as much accuracy and detail as our third-party ones, and hopefully even improve upon their models. But as many people seem to believe that privacy protects against toxicity, I feel the need to show that, historically, the effect has always been the opposite. One is free to simply not care that they are underperforming in casual content, whether their numbers are shown or not. Broad parsers invite certain conflicts early on to create conventions in their resolution where personal parsers keep them hidden for a bit longer, but extend and agitate the conflicts with that added time. On the whole, I believe that -- and psychological, historical, and sociological studies, including ones on game metrics specifically, all seem to point similarly in cases of partial ambiguity -- there is likely to be greater total conflict, and certainly more "toxicity" (which I'll define here as intentionally maligned behavior frequently sourced by animosity or defense-response, usually from trying to create distinction between oneself and "other" or to reject another side despite unclear, unresolvable borders) allowed for by personal parsers than broad parsers.
I'd be happy even just getting a page that shows how many unnecessary hits the party as a whole took, how many orbs it let through, how much damage was dealt, and how that compares to the damage necessary to clear gauged against expectations for the phases/durations covered, with a personal parenthesized contribution to those metrics of progress and mistake. The prior can in many ways shift the psychological focus away from oneself, especially if it reveals what's left to improve upon. I just feel that it would, in fact, be inferior in the long run to broad parsers, especially where every bit matters. And of course, this is all assuming that we can look at data graphs in order to figure out what can be improved upon (i.e. the fflogs level of analysis but in-game and at-will), rather than having just a final average. Without such, parsers can (deservedly, in my opinion) excuse the culling of players not pulling their weight as per the expectations listed in (or conventional to) the party's formation. But with such, the emphasis falls to optimization, and the skilled often feel a tacit obligation to improve, rather than merely remove, what issues the party faces in the context of the fight, specifically.