Not at all, look up the history of health insurance in America, companies providing it was not by design, it was in fact done to get around government laws on wage caps during the great depression.
Now days the system is entrenched, there are a large # of corrupt players who leech of the healthcare ecosystem in America, and they pay good $ to lobbyists and PR firms to keep things that way.
Right now 1/3rd of health care costs go to working out billing. That type of insane inefficiency would not be tolerated in a true capitalist marketplace. Imagine if Visa charged 33% commission on every sale and then had a law passed saying all purchases had to be done with a Visa card! That'd be an insane drag on the economy, America's GDP would plummet.
But we literally accept that exact scenario with health care costs. (Except for cosmetic procedures, which have a competitive market that has driven technology forward and prices down!)