I don't see a way round that, though, for the reasons I've mentioned. The NHS can't fund things that are not regulated, so they remain outside of its remit.
I understand what you're getting at - that people in your situation without the funds wouldn't be treated - but there are so many alternative therapies, some of which could be harmful, or might not cure an ailment in the same way as drugs would, and the NHS can't refer people to all of them.
There are also therapies that would be nice to have, but are not essential to a cure, so they would be considered in the same category as, say, a spa day - they might help to lift a mood, and make someone feel better, but they won't cure anything, so they remain an optional purchase.
Some therapists (eg sports masseurs) can get referrals on the NHS, but treatments such as aromatherapy or reiki can't, and I think that's fair enough.