Secularized Christian theme: interests of a social institution/Christian Church

About the state, state action and the issue of public interest. There are multiple problems here, which I am only slowly beginning to recognize. I will share two such problems with you without, however, being able to concretely spell out the alternatives. (a) Consider the belief that the state ‘ought’ to act in the public interest. This belief makes sense if we assume that it is possible to speak in terms of ‘public interest’ in some non-trivial fashion. Both Kenneth Arrow and Amrtya Sen have proved theorems that show that any such use incoherent: Arrow argued that we cannot speak of ‘public will’ in any coherent way; Sen argued that we cannot aggregateprivate preferences into a consistent and coherent set of ‘public preferences’. Our notion of ‘public interest’ includes these two notions and, as a consequence, does not allow of a coherent conceptualization. Even banning smoking in public places (whatever the notion of a ‘public space’ be) is not very coherent, if argued in terms of ‘public interest’. In this sense, justifying complex actions, which carry unintended consequences, in the name of public interest is not an interesting exercise. (b) Despite this, the idea of the state and its relation to public interest preoccupies people because of something else: that is the belief that every institution in society has an ‘interest’ and the state has a ‘public interest’. That is, there is an underlying assumption of ‘intelligibility’ to claims about “institutional interests’: each institution has an interest the way each individual has either a ‘desire’ or ‘interest’. The more I read history, the less intelligible it has become to me. I believe that this claim is a ‘secular translation’ of the idea that the Christian Church has some set of interests and political thinking, since the Middle Ages in Europe, has so constantly hammered on this theme that it has become a trivial fact that we take for granted. It is totally unclear to me how we identify the ‘interests’ of a social institution, the State included, and how we find out whether we are wrong or right in attributing such an ‘interest’ to a social institution. In other words, we have no clue how we solve our disagreement in this area of legal and political philosophy: the more radical the disagreement, the less clear how we should solve the issue: suppose I deny that the State has any set of interests that it can call its own, how do we solve this disagreement? On the basis of some or another definition about what ‘interest’ is or what ‘State’ is?