Well.... The game allows them to max their Cha & Int, and they can roleplay how they wish, so Genius, Philanthropist & Playboy are all well within their grasp. And Billionaire sounds like a background choice, so you might need your DM on board for that one, but I would want to be consulting my DM for any background of influence like Noble and so on to make sure it fits into their campaign setting.
Soooo.... Yes?
The players don't exist in a vacuum, stories are created by a group of players and a DM. So, again, what's the story that player wants to tell?
If the player wants to play a character who is all about the pursuit of power, then I would be advising them to build their character and their part of the game world in accordance to that. If the type of power they're seeking is temporal power, which is part of the larger campaign setting, then yes, they would naturally tell that story working in concert with their DM.
If the power they're chasing is magical power, and they choose a non magical martial as their character concept, perhaps they want to tell that story by amassing a hoard of magic items, in which case, yes, they will need their DM on board. Or perhaps they want to tell a story of longing for something they can never attain, in which case, no, they don't. Or perhaps in this case, if chasing magical power is the story they want to tell, maybe a magical class would be a better choice? There's plenty of room for lots of choices here.
I once played a fighter with 6 Con and low Str. I wanted to tell a story about an underdog triumphing against all the odds, a weakling succeeding where everyone told them it was impossible. It was epic!
If that's the story they want to tell, what's the problem?
No I said if two players WANTED to tell a story like that, they could. It would be awesome!
There might be only one King of England at any moment, but there could two twin brothers, identical in every way who are both princes, and heirs to the throne. Maybe there's a reason noone is sure which one was born first. They both vie for the crown. Different players might play them slightly differently which may decide which one succeeds. Maybe one is king for a while and then dies/is assassinated/abdicates for love /goes missing /is uncovered as a traitor and the other one gets a turn? So many epic stories possible!
Oh, was there a magic sword involved? Maybe. Maybe not. Hardly seems the point does it?