Well, yeah. They're basically a cult with three rules:
1. The market is perfect.
2. If the market is not perfect, then it's the fault of the government.
3. If you have any questions, see 1.
Austrians would also object to the notion of something being perfect. But they do analyze situations in which an external force interferes with the normal voluntary flow of actions and generally find that the stated outcomes (probably not the actual desired outcomes) of those external forces is generally not met. For example, rent control is often argued for as about helping more people to be housed and, empirically, that usually is not what happens when rent control is enforced. One could argue that the real intent of rent control is about making life better for the well-connected at the expense of the less well-connected and that probably does happen regularly.
1. Keynesianism: "Your spending is my income, so when there's not enough spending, the government needs to step in".
2. Monetarism: "The monetary supply directly controls the economy and is the primary reason for economic phenomena".
3. Austrian economy: the market god, the market is king, all hail the market.
The first two approaches provide actionable models and make predictions. As with all models, they have limits of applicability, and they are often wrong to some degree.
Meanwhile, Austrian economics is always right. And when it's wrong, it's because you haven't done it hard enough.
> If you think people in the market do things that are nasty when all the actions are voluntary (and that certainly can happen), shouldn't you be even more skeptical of those who are willing to engage in violence to force the things they want to come to be to happen?
Well, let's look at a particular example: pollution regulation. Laws limit the almighty Market by forcing compaines to clean up their waste.
Another example is monopolism. In the view of the Austrian economy "school" it is _always_ the result of government actions. And monopolies wouldn't exist otherwise, even for things like water supply and sewer.
The Capitalist Market is the One True God of America. All the math and waxing philosophic are just set dressing to make that idea less obviously absurd.
As for pollution, have you looked at the history of state run industries and their pollution record? How well does the US military manage its pollution, particularly prior to the EPA when the public consciousness shifted? How many of the worst private polluters were in the service of the government (such as for the military)? There are also tales of the communist countries and their abuse of the environment. And in the context of a democracy, one would assume that if it is faithful to what people want, then to have pollution controls requires at least 50%+ of the population to want them. That sounds like a strong market incentive to provide that not to mention actual destructive pollution can be subject to claims by those injured by the polluters. While it was before the largest amount of industrial pollution, there was a time in the US before the government got involved where pollution was restricted by such considerations. Companies did not like that so the government started to regulate in order to protect the polluters. Time and time again, actual government legislation is used to either protect the guilty or it comes in when 90% of a problem has already been resolved.
Also, the first two economic schools of thought you list do not make any basic sense. If it is just spending, then why would there be boom bust signals? Why doesn't everyone just keep spending? Something else must cause a reduction in spending which ought to be pretty important. If monetary supply is the only control for the economy, then set it and forget it on the trajectory you want. Since there doesn't seem to be a stable path, then some other factor is important to consider.
For either of them, why not just print up a million dollars for every person? Do you suddenly have a supply of million dollars worth of goods for everyone? No. There is real wealth that has to be produced and that is why futzing around with money is not good enough.
The information coordinating function is that of prices which requires a relatively stable money supply for accurate signals. If the money supply is artificially tampered with, then the entrepreneurs make bad bets, thinking that either there are more resources then there are (inflationary monetary supply, boom period) or there are less (deflationary monetary supply, spending contraction). The first case leads to half-completed projects when actual resources run out across the economy (bust). This leads to recession/depression which is a time to realign the resource allocation to what is actually desired if government stays out of the way. Compare the 1920 economic downturn (hands-off government, rebounds quickly) to the 1929-1940s economic depression (heavy government intervention under both Hoover and even more Roosevelt). In the second with deflationary, it is idle resources that are the result, they get cheaper, and eventually leading to a boom. There aren't too many examples I am aware of of this though there is a train of thought that the late 1920s had inflation (to help the British with their war debt?) and then the Fed reversed course and starting deflating the money supply cause quite the shock. In any event, both are examples of problematic time periods during the price readjustment to the new value of money.
The main reason the government inflates money is so that they can spend without explicit taxing (inflation is an implicit tax for those that do not get the first rounds of the money printed) and allows for the wealth to borrow to acquire assets, where asset prices inflate with the money supply while the debt burden deflates with inflation. This is specifically to help rich people get much, much richer.
Anyway, I don't see any way around not using math. Because value is subjective and that means it's a ranking system of preferences, not based in nominal values.
What makes the Austrian economics "school" a cult is not the complexity of models. It's their rejection of models altogether and a refusal to make testable predictions.