You're ascribing morality to a tool. That's like saying 'knives are bad because someone killed someone with a knife'. Parsers are a tool. Full stop. They're a tool. They, themselves, are not good or bad.
What is good or bad is how they are used, and how they are moderated. Which is the real thing that needs to be considered.
You just described most of the 'bad use cases' - but those can be mitigated by messaging and moderation. Going back to the knife example... we don't allow people to bring sharpened knives to certain places because there's not a lot of justification for them in those places. We punish people for using knives in certain ways as a deterrent to keep people from abusing the tool.
Same thing with parsers. By having firm messaging about how you can and cannot use the parse tool, by designing the parse tool to be positioned appropriately(ie. with a focus on your own personal numbers rather than others) and by having rules with specific punishments to deter misuse... you can mitigate the negative impact of them.
You describe the worst case scenario as if it's impossible to prevent... but it IS preventable. Knowing that those are the 'worst case scenarios', the team can come up with solutions to mitigate them.
ex. If the team makes it clear that it is against the rules to press someone to show their parse and that such behaviour is punishable... they make it clear that you shouldn't do that. They could also add a 'report for parse abuse' option to the in-game reports that would submit the chatlog for review to make it easier to report... just as one possible option.
The tool itself is not bad. The tool is meant for people to self-evaluate to help themselves understand where they fit in the game and how well they're performing. It can be used for bad... but to believe we can't have a tool because it could be used for bad is a level of pessimism I'm not comfortable with.