When something is paid for from a big nebulous ball of money rather than straight out of people's pockets, the downward pressure on prices just isn't there in the same way. The conversations between practitioners and insurers are about whether something is necessary, not about whether or not the practitioner is charging too much for it.
Here in the UK we see it, too - not so much in human healthcare since we have the NHS - but very definitely in animal healthcare; vets' bills have skyrocketed over the last couple of decades, in a mutually-reinforcing feedback loop with the rise in pet health insurance.