No-one knows how ECT works but psychiatrists still use it. (And it's quite bizarre - one branch of medicine is devoted to preventing seizures, another one busy causing them.) No-one knows how the medicine I have to take every day works, either. Glaxo still got a licence for it, and I'm very glad they did.
In fact most of modern medicine is not evidence-based. The EBM movement is relatively recent and only covers a tiny percentage of what healthcare professionals actually do.
I know GPs who offer comp. therapies to their patients. They do it because there are patients who need help and not enough tools in the standard toolbox. Living with chronic stress, chronic pain, cancer, all sorts of things, is ruddy hard. And maybe some medical interventions might help but then again they might not - it's often not as easy as 'hello patient, if we do X you will be cured'.
Surgery might be problematic, drugs contra-indicated or there just might not be a magic bullet for that particular patient with their particular mix of problems. People often don't come with ONE thing that's wrong, they have have several, which means they can't take standard drug A because their history means it's not appropriate.
Anything that relieves pain and anxiety is A Good Thing no matter how much people who aren't faced with patients in distress might want to scoff.
There is a reason why the Christie in Manchester has a complementary medicine service. Because living with cancer or caring for someone with cancer is ruddy tough, painful and stressful and complementary therapies can help.
Sadly medicine does not have 100% of the answers to 100% of the problems experienced by 100% of people. And even when it does have an answer, that can cause other problems. Drug side effects can be horrible, drugs can stop working, surgery isn't always possible and even when it is, you might not get a wonderful result - even when technically the op is a success. (I know two elderly ladies who are permanently disabled as a result of knee surgery.)