What's needed is less government intervention and more people shopping for normal health care to help drive down the costs.
That is nothing more than bald ideological nonsense in soundbite form with no actual details. The government HAS to be involved in medical care because the normal market forces do not work especially well. People are buying a product they don't understand well, from vendors who are very sophisticated, where it is typically paid for by someone else (insurance usually), and for which the customer (us) is in a very poor negotiating position (pay up or suffer/die). EVERYONE consumes health care and the only organization in a position to keep people from getting ripped off is the government. I don't have any great love of government but it serves a necessary role for some problems and public health happens to be one of them. There is not a single industrialized country on earth where the government does not play a very significant role in the health care industry. The notion that you are going to solve that problem by "less government intervention" (a meaningless soundbite) is frankly ridiculous. Let's hear your master plan for how market forces are magically going to come to the rescue if only the government would get out of the way.
Of course the typical collectivist response to this is "OMG you can't shop around when you're bleeding to death." Which is nothing but a straw man, because emergency and trauma care is a much smaller proportion.
It demonstrably is not a straw man. 50% of hospital admissions come through the Emergency Department. If you think that is a tiny portion of hospital revenue then you are delusional.
Even shopping around for the best price on a procedure would put tremendous amount of price pressure on the providers if more people did it.
That would be true if people were well educated consumers or if they had the ability or willingness to shop around. Unfortunately most people have an poor grasp of the nuances in treatment options or what constitutes a fair price. Many simply aren't interested in shopping around. When people are ill, they go to get treated to feel better. If you claim that you are going to go price shopping when you have an infection or nausea or a wound in need of prompt treatment, I'm going to call you a liar. Furthermore many people want to deal with a specific doctor that they trust and are unwilling to go price shopping even when it is an option.