Until we fix the collusion between the American Hospital Association[0] and insurance companies through the National Uniform Billing Committee[1] to opaquely set pricing, there will be no free market in the healthcare industry.
[0]https://en.wikipedia.org/wiki/American_Hospital_Association
[1]https://en.wikipedia.org/wiki/National_Uniform_Billing_Commi...
Further, while the technology has advanced (eg cancer treatment for your dog), prices are much lower than what humans pay, and in some cases, declining.
Namely: - Inelasticity: economic terms, human healthcare is extremely inelastic, you'll spend everything you have to save your own life. Not so much with a pet. - Poor information: Because of so many middlemen, there is very little information for human healthcare, you rarely know how much something will cost before you owe it. - Non-Fungible: doctors are not a commodity that you can trade out like cereal. There are human relationships involved, that make it difficult to compare apples to apples.
These are all factors that human healthcare lacks that are generally necessary to make for an efficient market.