Note, however, that I'm not asking here whether or not you can beat someone with PI. I'm focusing on whether it's an appropriate ability.
Would you allow for total immunities to other things? How about Social and Mental tracks? How about an immunity to Physical Blocks or Maneuvers(call it "Unstoppable Force" or whatever)? How about an immunity to assessments("Null Presence")? Or Declarations(Reality Warper)?
If any of those would be considered inappropriate, why do Attacks get a pass? What makes them special?
Appropriate? Sure. But you have to use your discretion in determining where it's appropriate and where it isn't. For example, that Ogre with physical immunity to mortal magic? Appropriate for a mixed group; the wizard might have trouble dealing with the guy, but he can provide support to the guy with the gun and the fae knight in your group. The BBEG with physical immunity to everything but one thing (ala Nicodemus)? You have to use that fittingly; unless you have someone who can break through his defenses reliably (like a Knight of the Cross), the point of fighting that guy is to delay him or get away from him. It's a GM's tool, and like any tool you have to apply it where necessary and put it away when it wouldn't work.
I'd totally allow mental/social immunities, but it would have to be a sensible thing. A golem or construct, for example, would probably have social immunity. I'd probably give mental immunity to something that simply has no mind. A plant, for example. As for the rest of the things you mention, it just goes back to how you use them. What's the purpose of shutting down those mechanics? If it's to create something justifiably dangerous and encourage your players to work towards an unconventional solution, that's one thing. If it's just to be big and scary and hard to destroy, then that's probably not a good use of the tool.