That's not true. Did the Alphas have to pay a price for their power?
No, they just had to learn how to use their magical potential.
If you want to have a human direct her magical potential towards being strong and fast and tough, you can. Just take an appropriate high concept and whatever Powers seem reasonable.
I've made characters like this before, though I'd have trouble finding one with an actual backstory. Most of the characters I've made are generic.
I'd have to disagree with this. There is always a price. Though I do agree with the thought that the price is probably on a par with the power gained. Part of the problem with making this statement one way or the other though is that we really don't have a complete picture of the Alphas. They are important secondary characters, sure, but still secondary characters.
My guess is that their "price" is a little of their humanity. Not nearly so much as a hexen wulf, of course, since there is no demonic element. But look at Billy in the last few books. Definite signs of animal aggression and ferocity. Not really a typical human response but not surprising from a person that has spent years learning to BE an animal.