Alternative medicine is permitted to exist by a single, yet fundamentally wrong assumption: that medicine is not science.
There is no alternative science, there is only science. That goes for math, physics, chemistry, astronomy, etc.. Strangely, people don’t accept that for medicine, as collective mentality is still stuck into the times much of it was mystical guess work, or came across that way.
Once you realize modern medicine is proper science to its core, there is no room for any “alternative medicine”, just as the Earth has only one moon and no “alternative” ones, water is always H2O, and we live in a heliocentric system.
An alternative (to) medicine is an alternative (to) science. We usually call that fantasy. When it claims it cures disease, the proper name is quackery.