That is... a lot to unpack, to be frank. I tend to try to integrate the non-economic philosophies of both thinkers into what I believe their understanding of the systems in question were, and by no means do I distill out anything necessarily useful or predictive, merely seductively correlated with what I've seen unfold in my lifetime.

However, so as not to disappoint, I will voice some opinions. I think there may be something to the Austrian school, and I don't necessarily buy Hayek's critics propensity for saying that he's trying to have his cake and eat it to as A) a reason to dismiss him outright and B) not a demonstration of the importance of his points with regard to the folly of trying to centrally plan an economy; something that I've recently come to realize we have been slowly degenerating toward in the United States. It just doesn't seem like it because you have to look at the meta-structure of decision making outside economics in order to realize the staggering shrink in the number of inputs to increasingly large chunks of capital as businesses undergo the process of merging and consolidation.

While the central planning we engage in tends to openly constrain itself to the money supply and interest rates, we still have the problem that there is precious little information truly at hand in order to make meaningful decisions. When decision making is distributed widely, you have a tendency for quick reversion to the mean to the degree that is most appropriate for the conditions in which economic activity is happening (Hayek point). The farther away you are the less fine grained your grasp on the the local aspects of the economic problem, but the greater your potential leverage, as when everyone looks up at you for cues, what you say has a way of going a long way (Keynes); not saying/doing anything, therefore is to actively make a non-interventionist decision, which means that spontaneous organization may happen, but not as quickly(Keynes' attitude toward action projected into Hayek's framework). Keynes seems to air on the side of doing something being better than nothing; as at least taking action in the long run tends to preserve some level of unity or at least preseeve momentum that can be redirected through policymaking as long as it is there, which I don't think is necessarily wrong. Though I think the Austrian's are safe in pointing out that odds are, you will make the problem worse by actively interfering and making decisions on which you have no information to safely make.

I've sat and watched QE deliver exactly what ABCT predicts. Regular interventions necessitated to forestall higher and higher stakes recessions that have spread wider and wider through the tighter and tighter integration between respective economies, and the rapidly centralizing tendency of merger friendly business environments. On the other hand, The prescription the Austrian's tout is unpalatable, or at least useful to me in that it insists the economy will sort itself out if you do nothing, so let the economy do it. I find in Keynes, however, that in the event of a crisis, you can shorten the recovery time by providing the judge required to get people to do the necessary business of transacting through stimulated demand. Economic activity (day to day life) wishes/needs to continue. However, the fact you're in the situation you're in leads me to believe that the Austrian's have a salient point. If you keep mucking with and distorting the market, instead of letting it stabilize on what it can sustain, you steer the economic problem into novel areas undeniably; just as undeniably as you set the stage for an eventual highly disruptive reckoning when the bubble bursts.

So what does it all come to?
I think the Austrian school of thinking is overall centered around the idea of the economy tending toward a distributed steady state driven by the non-human environmental factors, and the human responses to those factors. An Austrian economic model may end up leading to economic activity growing to fit it's container so to speak, but only slowly generate an overall increase in the size of the economic pie.

Keynesian economics, however, encourages risk taking and moonshots. Who needs sustainability within the container, when with enough economic oomph thrown at the problem, you can just right out of the container, get a second economic beach head going somewhere else, keep the size of the pie growing for everyone, and when things go south, pump every lever you can to get growth going in some new direction. The biggest issue I see with Keynes' system as a whole is the dismissal of Hayek's implicit assertion of a rational yet incomplete foundation for economics as far as the perspective of a practitioner is concerned.

So it does make sense to me the Austrian school is shunned, yet kept around like some voodoo doll by modern economists. It fundamentally undermines the field in substantial ways, but contains nuggets of how the non-macroeconomically inclined will fundamentally react in the abscence of active macroeconomic pressure.

That is to say, most people uneducated in economics at all tend to assume an Austrian model unconsciously. The Keynesian approach, while predominant, does not seem to line up at all with natural intuition without guided thought. Which ironically comes back to the two major differences in the two schools economic philosophies.

Hayek: Just leave it alone
Keynes: Do what you must to keep people transacting. If people feel nervous about where money is going to come from, drop interest rates. Once people are transacting regularly, start pulling the rates back up in order to control inflation.

Where both seem to fail nowadays, is in the consequences of smoothly bridging the transition between a highly interconnected growth optimized economy, and an economy physically constrained by the perception of elevated risk of death in the context of conducting the business of transacting. Neither model has any real oomph without people being willing or able to engage in business actdue to physical environmental constraints trivially.

For what it is worth, the Austrian's are neck to neck with the Keynesians as far as this latest crisis goes from my point of view. By doing nothing, the economy shifted to try to maximize its capability to transact whilst keeping the transactors specially separated. Depending on whether you view the coming stimulus from Congress as an act of monetary policy, or just the economy readjusting itself; you could safely make the argument that some of eitherschool is at work.

This is why I hate economics. It always seems to have had the answer in a post-facto rationalization sense, but it always seems to feel like a coin-flip making the decision of which way to go. Keynesian economics is probably the worst in terms of PR generators for economics though. If there is anything out there that makes people hate banks, it's the natural distaste that comes from someone else mucking about without knowing what they are doing. In that sense, you can't help but appreciate the Austrian's "your idea is as good as mine" approach.