I read the links you provided (except [0], which I do not have time for at the moment). I do not think Awodey and McLarty come across as well as you think they do, and I do not think Friedman misunderstands anything.
Moreover, you omit some of Friedman's best postings on this topic. The challenge is to show what advantages this proposed theory has over the standard foundations, or to demonstrate some interesting problem or conceptual issue that it resolves. I did not see any serious replies to this.
(Incidentally, the same challenge is my reply to the other comment to my previous post, about the ZX-calculus.)
Here's an analogy. Why do mathematicians consider groups interesting, but general Moufang loops not interesting? I propose the answer is that the additional generality provided by Moufang loops doesn't aid in addressing any interesting questions external to their theory. On the other hand, the utility of the group concept is obvious to anyone who studies a subject with connections to algebra.
This reasoning is roughly why the vast majority of mathematicians don't give two hoots about category theory, beyond picking up the few tricks like Yoneda's lemma that are actually useful. You can – as certain members of the category theory community have shown – take any mathematical concept, consider some generalization, and play various definition pushing games. But that's pointless without a good motivation (e.g. a concrete problem).
The previous two paragraphs concern "actual" mathematics, but similar remarks apply to foundations of mathematics. Friedman is pointing out that we already have a perfectly good foundational theory of mathematics and asking what gain we get by introducing categorical concepts.