In most countries the government is in charge of health care and they have a VERY easy way to regulate price gouging such as this. In any single payer system the national health service basically sets the price they are willing to pay and that's what it costs. End of story.
Well, not quite.
In any price control regime, the authority sets the price, and there are three options:
1. They HAPPEN to hit the "market clearing" price on the nose.
2. They set the price lower.
3. They set the price higher.
1. is a small target, and very hard to get right even if you're trying. (Even market economies only get there by constant feedback in the form of purchase decisions.) Further, there are strong political pressures on regulators on where to set prices, so they aren't even trying. So 1 just doesn't happen.
2. means the consumer gets gouged. (But now he can't go to some competitive supplier to get the product or service at a better price. EVERYBODY who is selling is selling at that price. So the gouging is institutionalized. The only way to get a lower price is to apply pressure to the regulators (see 1.) or go to a black market (with lots of risks, including issues of quality, reliability, contract enforcement, and bad encounters with law enforcement and the rest of the legal system).
3. is where the regulators usually end up. But a price lower than market-clearing means suppliers chose to spend their resources supplying something else, so the supply dries up. You could buy it at a sale price IF you could buy it at all. But it isn't available, so you can't buy it at any price.
A free market has its own problems. For starters, with a single supplier (a monopoly) market forces encourage gouging. With two suppliers they encourage an approximately even division of the market (a duopoly) and, again, gouging, with only price signals, not collusion, to coordinate their behavior. The incentive to engage in competition that drives the prices down to market-clearing level doesn't appear until there are three players, and doesn't become strong until there are four or more.
(Unfortunately, US regulations generally have a built-in assumption that two suppliers are "competition". Thus you get things like the landline/cable internet duopoly, or the built-into-channel-allocations local duopoly (collapsing to local monopolies) of the early, analog, cellphone system.)