The question is what do we do when we have an imbalance like this. When two characters are functionally identical but the system singles one out.
I guess that's where intention comes in. It is the part about choice that I have said earlier.
Sticking with the luck character, I can see 3 possible ways for this to work:
1. The character is just lucky, the player intents for the character to not take up any powers for now
2. The character is a distant son of a luck god, the player intents to not take up any powers from that
3. The character is a distant son of a luck god, the player wants to play out that part along the road, taking powers as they fit, but takes no powers at creation
1 is a pure mortal, no question about it.
3, at least to me, would be a changeling, no questions asked, but I got the feeling that there might be debate about that already. For me, the easy access to powers would be the reason for that. A pure mortal might be able to pick up powers along the way, but he would need a good reason why he can do it. A changeling can take up any power that has been agreed upon at creation, so it is a totally different animal.
2 is definitely up for debate, and here is where intent comes in. If the player just wants it to be the reason for his strange luck, but he wants to be a pure mortal otherwise, then yes, I can live with that, as long as the player can live with the consequence as well. If he suddenly points at his aspects and wants to take up a power, because his greatgranddaddy was a god, then I will point back to his template and tell him, that he agreed to wave that possibility at character creation. Of course he can change his template at a milestone, if he has enough justification to do so, but he would not be able to power up out of thin air.
I left out "is a pure mortal with the intent of taking up powers" deliberately. A character like that would be able to gather up powers of course, but only via milestones and solid justification from the story. And if he is a "pure mortal who gathered powers" at creation, he is no longer a pure mortal anyway.