Rich countries have highly developed sports infrastructures that allow better detection of talents and training the talents in the best possible conditions. That is probably already enough to explain the difference in results. No need to look for some drug conspiracy. If your city doesn't have the money to build a swimming pool, you'll never have swimming champions from there.

Russia, a powerhouse, had a ridiculously complex scam going and even they were caught.

They aren't rich in the normal sense, but they are powerful and secretive, so I think they provide a valid counterexample.

Does it go on? I'd believe constantly. Does it get found out? Every time, albeit there's always a short window of success. Do more powerful nations have more success at cheating? Yeah, since the smaller countries can't cheat as well.

But not a conspiracy, just correlation, I think.