"They don't need to avoid the perception of bias because they're free to run their marketplace however they want."
See there's two points this comment can be coming from, the first one is as a legal statement, like they don't need to do it because legally speaking there is no way that they could be forced to run their marketplace any way but the way they want, and it seems like that is what you mean - but the fact that governments exist means that nobody is really free to run their market in any way they want. There are always restrictions. And if someone were to think otherwise I would wonder what led them to think that.
The second way is as a moral viewpoint, which is what your next sentence "They have absolutely no obligation to look out for anybody's interest except for their own." also implies (as obligations are often referred to in the context of morality, while in a legal context we requirements are more often referred to - at least in the vernacular).
So which is it? Do you believe there is no way they can be legally bound as to how they run their marketplace, or is it just that you believe there is no moral obligation as to how they should run it (or ethical obligation, I actually prefer the word ethical in this case).