People don't go to these universities for prestige's sake, but for what prestige gets them. It's not really about the gold medal (for the vast majority), it's about being an elite athlete (i.e., being generally healthy and physically capable of impressive feats) and having the security to practice the discipline you love. Knowing that, you would build a network of schools that meet the full need of potential elite athletes, rather than rely on a handful of clubs and coaches. Which is exactly what we (and China, and the Soviet Union) did.