It's possible to be stacked and still skidding. The quad burn is a result of inaccurate for/aft balance. The skidding vs carving spectrum is controlled by edging and lateral balance. There are many cases in skiing where a deliberately skidded or shmeared turn is exactly what you need. To make this kind of turn well you need to be in balance and stacked over the ski.
As others have mentioned, it is possible to build up your muscles to a point where they can handle being over used. I see wall sits this way. Do enough wall sits to get massive quads and you can ski in the backseat all day with no pain. You could also learn to ski better and skip exercises that make it easier to ski inefficiently. I spent many years learning to be good at being a crappy skier. Those moves I practiced and learned have been hard to unlearn. I ski all day everyday and the only reason I can do it is because I finally learned to ski more efficiently. Practice makes permanent, perfect practice is what you need. Take a lesson from someone who knows what they are doing. I wish I had done it earlier!
Edited by tetonpwdrjunkie - 1/29/16 at 10:13am