Add a Parser that only the player can see.

[Spoekes]

Exactly.

People already parse you without knowing it.

You rather just remain ignorant to the fact that you can't reasonably play your job? I'm not talking about being average dps. But if you were pulling like 150-200dps as an ilv120 BLM or something, you wouldn't want to know?

You should expect that other people are already parsing you.

Exactly this.
Like I said before, if the parser was in the game itself SE would have full control over what is shown and where.
With the current status quo you get parsed, everywhere whenever someone has the program running.
The only reason for them not to do it seems to be that they are not willing to spend resources on it.