Yes, but that kind of healing is harder, if not impossible today. Two thousand years ago the relation of koshas to each other was different, the spirit still had greater effect on the physical vehicle. Thus miracle healing, healing directly by adressing ones' higher sheats, chanelling down healing forces was a possibility.
The idea, that human beings were the same all the time since 150,000 years, starting with homo sapiens (cro-magnon) man is false.
It is a common mistake of the sensorial mind. Like when they thought, the Earth is flat. Why did they think that ? Because waht they saw, was that the earth is more or less plane surface extending in all directions, towards the horizon. And, because they could not go far enough to realise that the Earth is in fact a globe, they projected their knowledge to the unknown. The same happens in case of materialist science. They know what the human physical body is today. They don'tknow (they don't want to know, as materialist scientific thought is prejudiced by so many thing the scientist does not admit, or often is not even aware of) about the other constituents of human being, like pranomaya, manomaya kosha, and they even question the ego, or the self, thinking it is only a product of the physical brain. Of what kind of product that could be they fail to explain, and they craft a theory.
Anyway, my point, that the rarity of such miracle healings today is caused by the denser nature of the physical body. If I recall well, Sri Swami Sivananda also talked about how very few able, healthy bodied humans do live today. Of course, young people appear healthy, but this is only up to an age. Health does not equal youth. As man ages, karma catches up. Few have so favourable karma what makes higher spirtual practices possible. Hence the need for healings, and diets, and yoga, and all sorts of stuff.
If someone is sick, due to unfortunate karma, the best is to expereince it, and develop the necessary soul qualities through this karmic process. Karma is not punishment, karma is a formerly accepted task with the goal of self-improvment, simply, karma is wise. (And unpleasant, but you already know that )