It surely is NOT impossible. When we finished our basement, I looked over all the options for putting in a floor, and I found a semi-aprung floor that was pricey but do-able. And it has worked very well, with no problems.
If I were to go somewhere for lessons, and the floor was veneer over concrete, I'd go elsewhere, no matter how good the teacher was. I'm not going to injure myself in pursuit of learning.
Jerry