For treating brain damage? No. Because no doctor would sign off on that as a treatment. There's no scientific evidence that oxygen therapy helps with brain damage.
Like most "alternative" medicines this one gets pushed hard as a solution for everything, regardless of evidence.
I have no idea. But if it's proven, available, and makes sense then generally it will be available with prescription for it.
That's generally the case with US insurance companies as well, which leads me to believe this is more "experimental" and thus not a good example of the merits of a single payer system.