Philosophically it is the most clear and believable economic argument and is best able to actually predict human action (which ultimately is what economics is about, human choice theory, and also the title of von Mises book).
The reason it is not as popular is because a basic tenet is that although we can study economic trends from the past, they are only historical facts and thus not open to empirical predictions.
This issue creates 2 problems for mainstream economics:
1). if we cannot predict, then economics is not a science like physics, but more of a social science. (and the profession has had achip on its shoulder since it realized this, and so has tried to avoid this idea, feeling economics is not as 'worthy' of a cause in academia).
2). if we cannot use detailed math (i.e multivariate calculus) to 'prove' economic theories, then we are not respected as economists and, more importantly we cannot do great 'new science' and thus academics can't publish a lot of esoteric articles and professors can't make a name for themselves.
Economics is not physics and never will be as scientific as physics. No matter how good your processor is, it cannot beat the Heisenberg uncertainty principle and so cannot acurately predict the timing and quantity of economic change, though it can predict direction of change.
I became jilted with graduate studies in economics, at what would be considered a highly respected university. I had the unfortunate luck of already having a good Austrian background before I got to the graduate studies.
Don't kid yourself, though, there were many professors who were very much Austrian in their philosophy, they just did other economics to build their name and shoot for their chance at the Nobel Memorial Prize.
Some Austrians remain amongst the winners of the prizes.