The example holds weight simply because I'm not debating legality, I'm talking about being informed, or lack of information. It's pretty much wording at that point. I could literally just say, "You could do x activity without x meter and you could probably judge the information pretty well. However without x meter you might possibly mess up in x way." It's not exclusive to a speedometer, or parsing, but it means the same thing, regardless of legality. You can do well, but if you don't have a precise readout on what you're doing, you're blindly hoping that you're doing the right thing.
This is important in the end-game environment because there ARE strict checks, and the difference between pushing a phase could just be switching up your rotation, or using a poison pot, or replacing a member. Knowing the actual variable which changed to bring about success is entirely ambiguous without a parser, though. You could push a phase, but not know why. You could be doing what you consider to be your 'best' rotation, but not meet the enrage timer. Could have been another player doing more DPS that pushed your phase. Could have been your poison pot. Could have been a weird amount of crits. If you're not meeting enrage timers, maybe it wasn't you doing poorly. Maybe another member was. Accountability is important, if you intend on being a part of end-game fights. Empathy is too, because your enjoyment is important, but when you're with 7 other people, there's is no less important than yours. Don't waste time. Don't stay uninformed because, "It's worked for me in the past." There's no good reason to be uninformed.
All of this still means the same thing for the pro-parse argument- Having more information does NOT hurt you. It's the information in the wrong hands, that does.
None of this changes the argument against having a parser in-game. The only adverse, or negative thing that it would bring in implementation, is a more widely available tool that people already use. There's no argument against keeping parsers out of game, other than, "I don't want the possibility of criticism". They can't protect people from something as vague as that, by with-holding something like a parser.