Indeed, it appears I was miseducated to believe there was more of a consensus that "free market" assumes approximately "perfect competition", when in reality there is a less of a consensus than I was taught -- e.g. modern followers/revivalists of "Austrian economics" are quite opposed to the idea of perfect competition being a condition of a free market.
Yup, because perfect competition is fundamentally the same as the salary cap, except for companies instead of employees. Specialization leads to natural monopolies at company level just as it does at personal level. Besides, the term monopoly only makes sense when it's state-enforced. In a free market it loses meaning since every company has a monopoly on their exact product.