"The only legit solution is the government, because they are the only ones without a profit motive in the whole system"

LOL. As you even parenthetically recognize, government doesn't magically solve humanity's capacity for wickedness.

The true "legit" solution is institutional legitimacy, which is fundamentally founded in a devotion to rational integrity. Genuine legitimacy can only be earned by sustained integrity, its not minted with the legislator's pen.

I agree that you're right to be concerned with the bad incentives of pay for play, but you appear to be missing the unintended consequences of imposing a regulatory monopoly.