I'd assume she only chose marked people because she wants to deprive the other Trumps of potential allies.

As far as why she didn't choose everybody with a mark... I know you're worried about Naoto, but I don't think it's as meaningful as you think it is. Kongou's vanished, probably into an dungeon. Mai's went missing during the jaunt. Leo is already helping out in her corner, I think. It's entirely possible that she didn't suggest Naoto because she knew she'd say no, or because she's more useful to her as a distraction, or because it would be too suspicious to ask of her, given her position.