A stab at a political liberal framework

Here is a little stab by me to formulate a political philosophy.

The political system would at its basis be a liberal one. It would not pre-suppose that there is a good life for everyone - society is already full of those. Rather, it should be a framework for coexistence among the different ways of life. In the words of Rawls, it would only be political liberalism, not comprehensive liberalism. I think the various forms of comprehensive liberalisms who become yet another sectarian doctrine (like Objectivism) miss the point of liberalism.

Why coexistence is preferable to war or oppression should be obvious. Our societies, especially in this age of migration, contain many views - both secular and religious - of what constitute a good life. It really makes no sense to prefer the option to coexistence. This is especially true of multi-national countries like the USA, Israel, Switzerland and Belgum, among others. But even in more homogenous countries, many different conceptions of what is a good life exist. The search for doctrinal unity in thought among humankind, or even among a single people, is a futile pursuit. That was realized in the wake of the religious wars in Europe a few centuries ago. Some parts of the world have apparently not realized it.

So far so good. Nothing of this is really controversial. In fact, most Western countries de facto operate on this basis to a large degree. So what about the rest?

I think the methodologies of both Rawls and Nozick to find this political framework are flawed. Rawls assert an original position, and Nozick make conclusions from a hypothetic state of anarchy. But why should we accept these? They're essentially skyhooks, conjured out of thin air.

A much better approach I think is to actually look at the real world. We don't need any skyhooks.

I've read the book Natural Justice, and it is essentially game-theoretic stuff. It is about how groups of people actually work, bargaining, fairness norms etc. I think it is better to take that into account rather than skyhooks.

Btw, is there any philosopher which have suggested any similar idea to what I've written in this thread?

So, what do you think of this derivation of a political liberal system? Is it hopelessly flawed, or is it good? Is it decent, but need some correction? Or whatever.