This really is the wrong forum to have this discussion, but here we are.
Your argument is conflating several issues.
The first question is whether we need more training positions here in the US. Yes, the number of applicants exceeds the number of positions available, but the vast, vast majority of USMD's and DO's all get spots, so what we're really asking is whether we should allow more US IMG's, or more non-US IMG's into the system. Which really translates to this question: "Do we need more doctors?"
That question is very difficult to answer. Some would say yes, and point to the patients who cannot get seen by a PCP because there are not enough. Or point to the fact that there will be lots of baby boomers getting older and more ill shortly. But others would say that it's really a distribution problem -- we have plenty of docs, just not in the right places. And training lots of docs to take care of the baby boomers doesn't make a ton of sense -- they will all die long before all of those new docs retire, and then we (might) have a glut. And this ignores the question of whether we should have more NP's or PA's to provide primary care (which is very controversial).
But even if we assume that we do need more physicians, my point above is that money is not usually the limiting factor. It's resources -- enough ICU time, clinic preceptors / rooms, etc. Those things can't be bought with money. Put another way, creating a system that stimulates programs to create slots so they can claim more money seems a really bad idea -- you're likely to get additional training slots in marginal programs that are just "out to make a buck". Although some programs have spots funded by a foreign government, this is very uncommon -- most programs don't want to get into that business because of all the possible conflicts.
And last, I'm assuming/hoping you don't need a visa. There is little question in my mind that any setup like this (you pay a third party, who then "funds" your residency, and then those funds are returned to you as salary) would constitute visa fraud for an H visa. The H rules are very clear that your employer needs to pay you a prevailing wage, and this type of setup is unlikely to pass legal muster. The rules for a J visa are less rigid, but I am concerned that the State Dept might still frown on this.
Anyway, the best of luck with finding a position.