Utilitarianism is often formulated as the claim: "The best society is the one with the greatest good for the greatest number."
There are many problems with this, first and foremost is that such an abstract formulation submerges the question of how to achieve and maintain this. To make this concrete, it doesn't even distinguish between radical capitalism and radical communism.
But another problem troubles it, one which crops up in multiple places in reasoning about moral societies: the problem of differing agency. Many of us understand on some level how troubling this is to the Enlightenment project of organizing societies, and this is evident in our discomfort discussing (for instance) behavioral genetics.
Here is an innocuous case of differing agency - one might call it trivially differing agency - that is not problematic for utilitarianism: I kind of like chicken. But my wife really likes chicken. If we get to the end of the meal and there's one piece of chicken left, the obvious best choice is to give it to her, because there will be more happiness in the world if she eats it. In the same way, I once refused a free ticket to a PGA tour event because I can't stand golf, and it is almost certainly true that whoever got that ticket instead of me, they enjoyed the event more. My taking up a spot at such an event would be an anti-utilitarian travesty.
Differing agency remains innocuous only so long as agents differ somewhat randomly in their specific tastes but not on average in the intensity of their pleasure and suffering. To illustrate this problem, Robert Nozick imagined a utility monster, that would always derive more enjoyment from everything. It doesn't habituate, it has no hedonic treadmill. You could imagine the utility monster as some kind of hedonistic superintelligent alien that had come to Earth to experience chocolate ice cream and massages, and experience them it does, on wondrous levels of ecstasy we can't begin to imagine. To it, we are as dim beasts, barely able to register pleasure compared to the raptures that the monster can attain. If we are true utilitarians, we always have to give our chicken and golf tickets (and chocolate ice cream and massages) to the utility monster. (Let's assume it's a nice utility monster that doesn't destroy things like the one below, it just likes the things we like, more than we like them, which is still a big problem.)
Not exactly how Nozick imagined it, but hey it's funny.
From Existential Comics
My gut reaction is that we don't have such an obligation, but I can't see why we shouldn't, if utilitarianism is correct.
Of note, Nozick also critiqued the Rawlsian conception of a just society, but there is a further critique of Nozick in the instantiation of societies of humans, which again relies on the actual differing capacities of humans that affect the quality of their agency. And despite heroic efforts to create equal agents, humans continue to stratify themselves based on these differing qualities.