I am close with Dr Gary Shreve who got his PHD in Operations Research Management and worked in hospital administration for his entire career. He actually did his thesis on assembly line functions in relation to healthcare.
The way he explained it to me is that healthcare costs are regulated to restrict company's pricing to be within specific profit margins.
The first issue with this is that it allows cost scaling so a hospital can spend 100k on machines when 10k would work just as well so the medical device industry makes an absolute killing. (Although that industrys margins are ensured because of regulation that prevents competition as you said.)
The second and main issue is that pricing for healthcare is not consistant. A person may have to pay 10,000 for a procedure but an insurance company has deals with the place so they only pay 7,000. Then theres a second insurance company that is 'in network' and only has to pay 4,000. Thats not really cool but the problem comes when prices are adjusted because the hospital can say "We are legally allowed to charge 10k for the procedure but over the last year we had 40% uncollected fees (from insurance pricing) so next year we need to raise the price by X amount to compensate." This allows scaling of healthcare costs every year which does not effect the insurance company but very directly effects the individual.
You can see this pattern in citys now. Everywhere you go there are 24 hour urgent cares and hospitals flying up. Granted that explanation I gave we me regurgitating a conversation I had on the subject to the best of my recollection but I personally think the elimination of insurance would be far better than subsidized or mandated insurance. Or they could simply force pricing in ratio to profit as a price ceiling which would solve everything : )
And if you really think about it- there already is 'free healthcare.' Hospitals can not deny care in America when it would result in loss of life, limb or eyesight. When they provide those services to all the overdosing hobos for example- the cost just gets spread to everyone else through unpaid taxes and raised costs the next year.