What do you do about greed? Rich people that exploit the poor and end up controlling everything? The bankers?
I would not worry too much about that. Free markets are to remain that way. Any action on the part of any corporate entity that demonstrably thwarts or otherwise alters the organic nature of the market has committed a crime and would be given a stern lesson in screwing around. The shareholders would pay a substantial part of that price and would thereby be enjoined to take a more active role in overseeing the managers they hire to run their businesses. Corporate managers convicted of such crimes would, as with any criminal, spend time in a prison that would make them cry like children. Even if they spent only two years in the klink, they would be so straightened out at the end of it that they would sooner eat their own guts than ever risk a second helping of solitary confinement.
Were I king, prison would be a horror. No violence against the prisoner at all. Just an 8x10 cell arranged such that the prisoner neither sees nor hears another human being the entire time they spend there. No outside communication of any form, not even with a lawyer, who would have to handle his client's appeals on his own. By the time a year had passed, they would be so averse to ever violating the rights and trust of others, most would never again pose any threat to the rest. The silence would compete with hell itself. No books, no photos, no amenities of any sort. Aobominably balnd and flavorless food is delivered by machine. You keep your cell clean or your sentence is extended. You are under 24 hour surveillance. Any time in the infirmary is not credited to your prison time, so you are motivated to remain as healthy as possible. I would make sentences shorter than what is typical precisely because the time is so hard.
Greed is not a problem in and of itself. All we need concern ourselves with is the behavior of the sorts of people you cite. If they violate rights, they go to hell. It is a simple formula. Anyone falsely accusing such a person sees a similar fate. Anyone knowingly participating in a frame-up wins double the sentence handed down the falsely accused, forfeits their entire material wealth to them, and makes whatever other restitution the law might require.
In my world there would exist fabulous carrots, available to one an all for the earning. There would be horrors awaiting those thinking themselves entitled to violate the rights of anyone. One's fate would be entirely in their own hands. Corruption by any "government official" would earn triple the customary penalties, or even death. Anyone assuming government office, epecially if elected to it, forfeits some portion of their rights, particularly when discharging their official duties. They could be surveilled at any time - privacy would go out the window. That is how it would be. I suspect there would be very few career politicians. In fact, I'd be willing to bet there would be none. Those assuming public office would do so a short stint because they really believed in what they were doing. Pay would be humble and the penalties for corrupt acts terrible. You do the math.
Corporate entities would enjoy certain granted "rights" as they do today. Corporation are not persons and therefore any "rights" they may possess may be so possessed only at the pleasure of the law. Therefore, those rights may be altered under conditions that would have to be codified in law. Abuse would result not only in punishment for those persons responsible, but possibly to the corporate "person" as well including abridgement of those privileges (AKA "rights"). Because a corporation may become a super-organism that wields super-human powers, they are to be subject to certain controls such that fascism would be a highly unlikely outcome. Fundamental rights belong to individual people ONLY. Corporate "rights" are bestowed by way of principles. Corporations would be protected by all due process, but their prerogatives would be somewhat limited when compared with the fundamental rights of people.
The other side of that is this: if silly Billy Gates invents a better mousetrap and the world beats a path to his door and he corners the mousetrap market, barring any criminal activity on his corporation's part, he is it. So long as he commits no provable crime against the rights of others, he will own that market. In truth, if that market proves profitable, chances are slim to none that he would be able to monopolize it. Barring very specific and unusual circumstances, any market that lucrative would become target for competition. If silly Billy was discovered to have set up barriers to entry such that competition would not be able to get a foothold in the markets, he would see prison time and his corporation would be taken to the cleaners. To beat the already dead horse, in my world committing crimes against people would be handled most unequivocally. I would strike white terror into the hearts of those who saw fit to violate our rights in criminal fashion.
