Criticizing Hazlett of being too rhetorical, while typing a wall of text without a single objective refutation to one claim is hypocritical at the least. It sounds like you don't want to stick your own neck out and make an incorrect statement.
I don't see why one needs to refute a text to point out that polemics written by authors who eschew the use of conventional economic methodology is a less than ideal introduction to economics for the uninitiated. Its like pointing out the writings of Seventh Day Adventists aren't a particularly good introduction to Christianity, particularly when it comes to understand what Catholics believe in.
If you want a specific examples of arguments omitted he criticises inflationary policies at great length whilst ignoring the underlying reason for favouring some level of inflation (incentivising investment)
The real problem Hazlett ignores is the existence of market failures in the actual world. The labor market in particular is rife with failures, in areas from search costs to market power, to the point where many labor economists model the labor market as a monopsony, i.e. a single-buyer market, which is one of the classic situations where government intervention to raise prices can increase total surplus. There's a whole discipline of labor economics that deals with the fact that the labor market is imperfect in excitingly complex ways.
In general a real market is imperfect in any case where firms make profit above their cost of capital -- i.e. most of it -- since perfect competition is supposed to drive profits to zero everywhere. The employees of a firm making profits certainly can be paid more without imperiling production, since the profits could simply be reduced.
Almost throughout, Hazlett makes exactly this (very common, for those with a political axe to grind) fallacy, supposing implicitly everywhere that no company is profitable despite the fact that we are manifestly not living in that world.
In general a real market is imperfect in any case where firms make profit above their cost of capital -- i.e. most of it -- since perfect competition is supposed to drive profits to zero everywhere.
This is simply false. You are confusing profit with economic profit - they aren't the same thing. Profit is revenue in excess of costs, while economic profit is risk-adjusted profit in excess of other investment opportunities.
I.e., in a noncompetitive market, your best investment is to seek out companies with high economic profit and invest in them. In a competitive one, your best investment is a diversified portfolio indexed to the broader economy.
Incidentally, monopsony models of the labor market have pretty terrible predictive power. They are loved by PhD holding activists since they justify many feel-good policies, but they don't work very well outside of certain narrow fields (e.g., PhD chemists).