Listens-To-Winds does have some capability in this matter, but he's a Senior Council Member and regularly goes back to medical school.
I think there are two sides to this. It's not only the caster himself who has to know precisely what he is doing, but the patient, different from what regular medicine can do, has to let it happen to a certain degree. If he doesn't, I think it acts sort of like a threshold (not linked to a special skill, just an inherent part of a human being that allows him to withstand magical changes to his body), reducing the effectiveness of the spell. Since the healing spell itself already requires a lot of power, an unwilling patient will make it pretty much impossible for all but the most dedicated of mortal practitioners. Fae, if they have a hold on you through a bargain can either ignore this or can simply overpower this inherent threshold, like Lea did in... I want to say GP?
And I'm not even talking about actively and willingly not consenting, I think it can be subconscious. Trust can be a real issue, for example. The two "healing" spells Harry gets in the novels from mortals are the reiki spell from Elaine and the stone necklace from Eb. Both are people he trusts, even though there are some tensions between them. And even they couldn't actually heal the damage, just make it less worse. Very few people will actually trust a stranger enough to let him rummage in their insides to get any real healing done. Listens-to-Wind might actually be an exception, because, at least in the white council, he has built a reputation as a healer, and I'd wager that a lot of wizards would trust him enough to at least let him help a bit.
At least that's my interpretation of the narrative limitations of healing magic. Of course you can do rituals to temporarily gain recovery powers, and I don't think from a mechanical standpoint they even have to be too complicated. A few aspects, and you're done. But getting those aspects is going to be tough. I would not accept any old aspects. Phoenix feathers, water from the fountain of youth, and so forth. It's going to take a while to get ingredients like that.
Over all, it's simply going to be too tedious to deal with something like that. Mortal medicine will stitch you up just fine, and as a wizard, you have enough time to let a broken leg heal for a few weeks. Not to mention, that it heals perfectly in time, just because you are a wizard. In the short term, it would be quite helpful, of course.
If you want to play a wizard who has mastered self-mending magic, you can easily let him take a recovery power and be done with it. If you want him to be able to heal his allies as well, allow them to take the recovery power as well. Instead of them having inherent magical healing abilities, you can narrate it as the wizard brewing a potion designed specifically for each of them, that they take regularly, that enhances their bodies self-healing capabilities. Or that the wizard has linked them in a biomorphic field that allows them to heal quicker. Or anything like it. As long as you have a good explanation, it'll work quite nicely. And it is ripe with compels, of course.
Basically, if the players want to heal quicker, I think it is reasonable to make them spend the refresh to do so. If they have a good in-game explanation, there should be nothing against them taking the powers.