At the top level of any sport, the expense comes from the coaching, exercise science, travel and other support over the course of years. That's true whether the game is cycling, or football. A $20,000 bike is peanuts in comparison to this cost. Unless you are at the top 0.001 percent of cyclists, better/more training has a much bigger impact than gear. $1,000 gets you a competitive road bike that you can win your local races with. Even cheaper if you buy used.
> From what I read about China, they're constantly scouting primary schools for Olympic talent, so you can come from any background and reach the top in a sport that would be limited to wealthier people in other countries.
This is what wealthy countries do as well. Most wealthy nations have programs to identify and develop top-level athletes. An obvious example being the very lucrative scholarships offered at American universities.