Not sure what Olympics you guys watch, but the one I watch for sure has a restriction as to how many competitors from each country moves on to finals, or even gets to compete.. As does a lot of world championships.
The three per country rule is in fact in place, and is a part of iasf, anyone not agreeing with it has an abundance of usasf division to choose from. No one is being forced one way or another. If teams knew they would likely only get to compete once, there is no attraction to fork out the amount on money it actually costs to go. It's not only the travel cost, but also accommodations, food, and competition fees. You have to remember that you can probably count on one hand the amount of teams outside of north America with any type of paid bid. (so even though flights might cost the same from Cali and Jamaica, most Cali teams gets a part, if not all, of it paid by usasf)