Hmm, maybe I didn't clearly make my point. Sure, getting strings on people in return for gifts is a fine representation of gaining power over them. Mythological demons tempt mortals with various things, vices if you will. Succubi specifically offer sex, and commonly drained or captured something from their victim- life energy and/or/i.e. semen. If you're adding the faustian ability to grant other gifts, I'd say Infernal Gifts would be the Succubi sex move. Perhaps that's what you are hinting at with 'time and intimacy'. This is what I meant by a price, I suppose- give yourself to the Succubi in return for... well, usually in the mythology, just the wanton sex. They are muy sexy, but take something in return for the pleasure.
Succubi seduces you, you have sex. String gained on you, and the sex makes you feel great. I could see the partner getting to choose from a list, like lose a condition, heal a harm, get a string on someone else- something to keep them hooked. But they'd maybe also get a condition like drained or sex addict or similar. Then maybe the Succubi has additional options to spend a String on people with that Condition.
There might be a productive approach in enhancing Turn Someone On as a move, perhaps adding a mechanical incentive to the target to 'give themselves to you' or making it an additional option on a 10+, with incentive for the target (XP?, but you'd need something for NPCs).
Just my thoughts on the skin.