A simple question can demonstrate the absurdity of his approach:
Can you sit in an armchair and use deduction from the action axiom to determine how all prices are actually set in real world capitalist economies and with apodictic truth?The notion that anyone can do this is just ridiculous, and anyone who claims they can would quickly be shown to be deluded and mistaken.
One can no doubt construct abstract analytic a priori models, but those models must be given an empirical hearing and checked against reality to determine whether they do in fact describe the real world.
The point is that the really interesting and important questions about real world market economies can only be determined by hard empirical research and study, not by mere deduction from a few trivial axioms.
For more on Austrian praxeology and its failings, see here.