You are completely misunderstanding.
I'm not advocating that Price go out there and start relying on doing the splits. However, Price is going to have to learn (as will most goalies in the league, in juniors and levels below) that you have to come toward the puck rather than recoil, you have to elevate and lean your body forward + over the puck to eliminate the elevation of the puck into the upper portions of the net.
Price has the advantage of a very tall frame, if he gets out and takes the appropriate leaning angles against shots, literally very few shots will be able to beat him up high.
Quick's philosophy is the appropriate one. Price doesn't have to play LIKE Quick but he certainly has to employ the same philosophies because they are the correct ones. Price's style right now involves a lot of play from his knees, not just being low to the ice like Quick, but on his knees, he completely neuters the strength of his legs and as a result is dead in the water against quick pass plays, pass-outs, board bank shots, blocked shot rebounds and one-timers.