In order to understand this, it would probably be a good idea to read Dr. Chartier's post and the comments that have already been published on it, particularly this one (since this post is directly a response to that comment).
If I understand correctly, Hobbes sees the sovereign as existing to settle conflicts. In Dr. Chartier's post and comments, he's seemed to somewhat equated this to a notion of "preserving civil peace." And to an extent, this makes sense. With property disputes, for example, what the sovereign is being asked to do is to merely uphold some exogenous system of justice: the sovereign is just acting to make sure we maintain a peaceful environment, where we get our idea of "civil peace" from somewhere else.
But to Hobbes, this will treat too much as settled. He would likely want to say that we may disagree on what it is that even constitutes "civil peace." One person might have a desire to see all homosexuals put to death. Another person might have a desire to see his homosexual compatriots protected from this fate, and is willing to fight to defend them. Another person might want to see the bigoted guy put in the stockades for being such a jerk. Hobbes thinks that this kind of conflict is a serious problem. In the absence of any external norms and institutions to tell us who is right and who will get their way, and in the absence of any enforceable agreement between them, Hobbes thinks that the three people in our story will have no reasonable choice but to prepare for violence. So long as each relies on his private reason, they will be condemned to a state of war.
The liberal solution to this problem is the one which gives us the notion of "civil peace" that I imagine Dr. Chartier has in mind: this approach typically seeks to independently define some conception of right-of-way, so that we have a way of adjudicating disputes according to these independent norms. But Hobbes doesn't have this machinery in his system. He could say that there may be no standard of right-of-way that each of the three people in our story would accept if each relied on his private reason. The system of rights and duties that will appeal to the bigot will be seen as oppressive by the defender of the homosexuals, and vice versa. And even if they could strike an agreement, there's no guarantee that some new issue won't arise in the future to drive them apart. The only way for them to avoid the state of war, Hobbes thinks, would be to give some third party the authority to choose what constitutes the appropriate conception of "civil peace" that will underpin their society.
The problem with the limits Dr. Chartier seems to want to place on the sovereign, I think, is that it seems to be in conflict with Hobbes' desire that the sovereign have the authority to decide basically everything about how a society is going to function. If this authority is denied in areas where there could potentially be legitimate disagreements between people, then Hobbes is going to worry that conflicts will arise, where each side believes that his own private reasons are the right reasons. Hobbes wants to eliminate this possibility by giving the sovereign absolute authority to decide what's right and fair.
But all of this is drilling way further into Hobbes than I think Dr. Chartier was seeking to do. If all he wants to take from Hobbes is the idea that a government is necessary to adjudicate disputes, then none of these issues are going to be a big deal. In this case it seems to me that he's actually moving away from the substance of Hobbes' argument and actually moving closer to the sort of thing Locke was saying in chapter 9 of the Second Treatise. As Locke writes:
Thus mankind, notwithstanding all the privileges of the state of nature, being but in an ill condition, while they remain in it, are quickly driven into society. Hence it comes to pass, that we seldom find any number of men live any time together in this state. The inconveniencies that they are therein exposed to, by the irregular and uncertain exercise of the power every man has of punishing the transgressions of others, make them take sanctuary under the established laws of government, and therein seek the preservation of their property. It is this makes them so willingly give up every one his single power of punishing, to be exercised by such alone, as shall be appointed to it amongst them; and by such rules as the community, or those authorized by them to that purpose, shall agree on. And in this we have the original right and rise of both the legislative and executive power, as well as of the governments and societies themselves.
If Dr. Chartier is considering this sort of approach to thinking about government, then yes: I agree that it don't establish a whole lot about exactly what a government is supposed to do or how big it needs to be. As long as it addresses the "inconveniencies" of the state of nature, any system of government will seem to do, and insofar as a stateless, decentralized, or pluralistic system can address them, that would be fine too. But this shouldn't surprise us: this Lockean position is what underpins a great deal of the modern libertarian tradition, including Rothbard's market anarchism and Nozick's decentralized, pluralistic vision of Utopia. I should add, though, that it also shouldn't surprise us to find that we're led to conclusions very different from those that Hobbes professed.