Home Depot would happily gouge you if they could form a cartel and gain enough control of the supply chain.
This is, after all, the reason we tend to avoid government monopolies if we can avoid it. It's not just that government is inefficient, it's that monopolies are inefficient, whether "private sector" or otherwise.
There's nothing peculiar about medical supplies that make them easy monopolized. Pharmaceuticals and medical devices (neither of which are the topic of the original post) enjoy patent protection, but there are often many out-of-patent substitutes available.
Doctors are limited, but that is primarily because the state makes it illegal to practice "medicine" without either being a doctor or being supervised by one. Much other scarcity stems from this one, e.g. limited insurance options because it's difficult to create a physician network.
There are absolutely free-market-advocates out there who would remedy price-fixing problem by allowing self-taught people practice medicine. That should increase enough market-entrants to break any cartels we see.
I'm not one of those advocates, because I see some sort of quality guarantees as helpful in this arena. But there are lots of aspects of the healthcare market that could benefit from more market-like behavior, whereas there are other aspects which could use less (i.e. more regulation). We need nuance in order to make progress.
I do very much believe more consumer choice for non-urgent care would be helpful, i.e. lab choice, hospital choice, a menu of drug options (ratings, side effects, out of pocket cost). This is controversial for a number of reasons, but after considerable, I believe this would have significant positive impact on the overall efficiency of healthcare.