Marxism took the same approach--attempt to derive absolute truths about the empirical world using pure logic. I don't know if Mises actually applied Hegelian dialectics, but the fundamental approach seems similar. It's all very German--compare Einstein's approach where he generates imaginary paradoxes and then finds higher truths in their resolution.
Problem is, the real world is messy. Some aspects of the world are susceptible to logical reductionism, but not all of it. Enough of it is arbitrary that you very quickly fall off the rails, even when it's not obvious. A theory can often seem superficially more consistent than it really is simply out of coincidence, insufficient precision, or insufficient predictive power. In the real world the proof is in the application.
Problem is, the real world is messy. Some aspects of the world are susceptible to logical reductionism, but not all of it. Enough of it is arbitrary that you very quickly fall off the rails, even when it's not obvious. A theory can often seem superficially more consistent than it really is simply out of coincidence, insufficient precision, or insufficient predictive power. In the real world the proof is in the application.