Yes. It’s all very plausible sounding, neat, and internally consistent, but you can’t derive a useful macroeconomic model from it that matches real-world, empirical observations. (Of course, the same could be said for a lot of mainstream stuff).
Part of it is probably just the historical context - monetary systems in the modern economy are very different than the gold-standard, fixed exchange rate kind of environment the book was written in, for example, which changes a lot of how things operate. But even then I think it still would have suffered from the fallacy of composition, where you can’t start from a description of interaction between two people and just scale it up - the emergent behaviour is almost always surprisingly different.
Could you provide a concrete example where it breaks down?
With regards to Austrian economics, as far as I remember, the school is not even mentioned in Hazlitt's book, but you are right that he was heavily influenced by it. But the book and its propositions stand on their own, I think.