And if you instead had a player come to you and say, 'I would like to play this really interesting character that I've worked out, but I don't want to be overly punished for it mechanically, do you think we can come up with a way to work around the rules to keep the game satisfying? I only ask because I get kind of bummed out when the story says I'm this awesomely skilled exemplar of mostly-mortal kind, and yet end up failing at everything I do because of some technicality that says I have to suck, especially in comparison to the other player's characters...'
What would you say then?
'Screw game balance and player satisfaction'?
Well, I think first I'd say that you really should take a look at the rule book, having two less stunts or two less free refresh really isn't going to make that big a difference on your characters effectiveness. Also, I think you're characters background is awesome, and I promise I'm going to make sure it pays off in the story. But yeah, +2 Refresh comes from being Pure Mortal, not from not having powers, so if that's not what you're looking for then you may want to re-jigger your character.
Of course by your logic, if I come into your game and say, "Hey, I've got this great character concept that I love. His name is Steve and he's an 80 Foot Fire-breathing dinosaur, I'll buy all the large size stuff and all the powers appropriate. But here's the awesome thing, he also runs the local coffee shop. ... Oh, no, he's always an 80 food monster, the locals call him tiny because they think it's a funny nick name for such a big monster." That would be cool with you right? Because I mean you don't want to limit at all the types of characters you allow so long as they're in RAW.