at which point, bringing up every failure of free markets (like, obviously, US healthcare) is dismissed as "not really a free market"

I mean, it's not. In a free market you'd have a choice of insurance providers rather than having to take whatever plan your employer offers, and you'd have some idea of what the hospital is going to charge you beforehand rather than receiving random bills for weeks.

Just to be clear, my definition of free-market is just that there is no centralised authority that can use force to set prices/quantities/quality/type of services offered. Of course, the fact that the employer has to offer health insurance in some cases is part of it not being a free market. But there are more fundamental things that make the US healthcare very far from being a free market. The first one is that the supply of doctors is capped in quantity, not just in quality.