Instead of denying objective truth, can't you get the same benefit by making your claims precise enough that they only talk about one system?

When I read what you write it's unclear to me what this has to do with postmodernism. I imagine that you wrote it without engaging with postmodernism. Wilbers work seems to me to have little to do with the postmodernist project.

I don't see how acknowledging that different models work in different contexts necessitates giving up the search for objective truth.

Let's say that in order to reduce complexity, we separate Physics into two fields - Relativistic Mechanics and Quantum Mechanics - whose models currently don't mesh together. I think we can achieve that without appealing to subjectivity, or abandoning the search of an unifying model. Acknowledging the limitations of our current models seems enough.

If culture does not have any common ground which binds them together, it simply disintegrates. You are essentially for atomization of society actually. If you rip apart different parts of culture, and they stop making sense to each other, same will happen with people.  Without a common narrative, a myth, it is impossible to keep society together.

To frame complexity as a problem is like "I am not smart enough x problem therefore how about I pretend that there is no x." 

Nations and peoples are bound together by common myths, common cuisine and common survival strategies. These uniqueness create a bond, a familiarity. Destroying this is effectively destroying people.

You should take a look to the Early Greek history and especially focus on Polis.