The Olympic committee killed the amateur rules in 1983, because a lot of the Eastern block was using "professionals" already, and it stopped a lot of western middle class athletes from being able to train and earn a living. The different sports federations (which set entry rules for their respective sports) followed suit in the following decade.
As for "overpaid professionals", US basketball isn't the only culprit. Soccer has a bunch of those from other countries. If you ban them (because you think they make too much money), then you'll also ban the women of the WNBA who don't make much, or a bunch of the other sports as well.
What they Olympics want is the best, and the best are usually pros.