I suggest that you guys might be overthinking it slightly.
Characters with free will have a Refresh rate. The ones who don't, don't.
At the very least, it means that starting a game with a PC without free will, you start with 0 fate points. Whatever compel the GM first throws at you, you have to take it, because you lack the FP to buy out of it. You will probably also take the next couple compels, so you have them to spend in a big fight, or to buy out of a compel at a more crucial moment so you don't give in to your urge to eat your allies or whatever.
And now you're back to being starved of FP, so you have to take the compel eventually, or even start self-compelling. Rinse and repeat.
Observe how very, very entrapped by your lack of Refresh your character is.
There we go.
It now merely gets into which Aspects the GM will compel to make life difficult for you, and how. If it's agreed at your table to go easy on the Aspects which might encourage back-stabbing allies, then you can totally have a varied party (Blampire, pure mortal, true believer, etc.) working together, sure. Stranger things have happened in real life.