No, it's not. It's a representation of the greater degree of free will Pure Mortals have as opposed to supernatural creatures. Still, I don't entirely disagree, removing it for purely thematic reasons doesn't quite work out.
Mortals who've placed that much faith in a particular deity have given up some of their free will to the deity in question. This seems both reasonable and appropriate. Michael and Father Forthill have a lot less freedom to act than someone who isn't working for their boss, y'know?
The White God is all about enhancing and promoting free will. He doesn't take it away.
Anyway, this sort of thing is easy to come up with if you're starting from the assumption that Refresh makes sense as a thematic thing and then working to justify that.
But no matter how many justifications you come up with, the cracks in the original idea will show through.
Why does becoming famous for my sword skills (stunt moving Reputation to Weapons) reduce my free will?
Why does training to become a great locksmith (Burglary stunt) reduce my free will?
Why is my free will affected by the number of people who know that knives soaked in moose urine are deadly to me?
I can come up with this stuff all day. If you want to justify it all, you'll have to twist your definition of free will into pretzels.
The Refresh-freedom thing only works in a very broad sense. It totally collapses when you look at it point-by-point. So you shouldn't use it to back up specific points; it never works at that scale.
Prohibit? No. There'd need to be some rule remotely allowing it for that. There's really not any support for any Sponsors other than those of Sponsored Magic. They're perfectly balanced, but very much not a part of the RAW.
There's as much RAW support for non-magical sponsors as there is for the existence of a character named Alphonse Whitwell.
Being sponsored by the police is no less RAW than naming your character Alphonse Whitwell.
Uh...actually, never needing an emergency room or other justification to recover from damage is something that comes up...and potentially pretty cool. Not 2 Refresh worth of cool, I admit, but it's not useless.
I guess whether it's useful depends on the game.
Thing is, either the Power is inappropriately costed at 0 or it's inappropriately costed at 2. Can't be fair at both costs.