> data to validate it.
You've accidentally illustrated the disconnect. Because the fundamental disagreement between the Austrians and the more mainstream academic schools of thought is epistemological. Data can only settle differences when both sides agree on the epistemological ground rules.
I have an advanced science degree. I'm not afraid of math, and I've plowed through Keynes "General Theory". It doesn't come close to passing the sniff test for basic scientific rigor. It can't.
Economists can't control their variables, and they have no way of knowing what their error bars are. They can make empirical models that work most of the time, but they can't know what regime those models are valid for, and where the breaking point is. There is every indication that economic systems are chaotic, and prone to sudden discontinuous phase changes.
Worse, unlike a chaotic system like weather, the underlying primitives are not at all primitive. We can say very precisely how a cubic meter of air (for example) behaves under widely varying conditions. This is why our weather and climate models keep getting better -- you can use more processing power and better algorithms and use the basic laws of physics to get the right answers, despite a system of incredible complexity.
But economists have nothing like that to work with. There is no meaningful sense in which we have good statistical models of human economic behavior. We have very limited snapshots, that are invalidated the moment customs or conditions change beyond the originally observed regime.
All of this means that you can't even build empirical models unless you have a preexisting, a priori theory of economic cause and effect, and you have no experiments strong enough to falsify bad a priori assumptions. The Austrian argument is simply that all economists are actually engaged in a priori theorizing, despite their protestations claiming to be empiricists.
I find the assertion that the Austrian school is more "intuitive" and accessible to be silly. Nobody who has actually tried to study the primary texts would claim so. It takes a pretty strong background in philosophy just to follow the first several chapters of Human Action -- precisely because they focus on epistemological issues.
It doesn't require a conspiracy theory to explain the popularity of econometrics. Lots of social sciences spent the whole 20th century pretending to be as rigorous as physics and chemistry, to bask in the reflected glow of progress. Nobody likes to admit that their field has no experimental lodestone, and so drifts along as a popularity contest.