Very hesitant that this is the actual problem of healthcare. What you care about is not how much the hospital bills, but how much is leftover after insurance. And that is unknown to all parties.
This might help a little bit, but there is no silver bullet.
A silver bullet would consist of introducing a single-payer system and winding down the HMOs.
Putting that burden on the individual is akin to a reverse lottery, where an unlucky few pay are forced to pay obscene bills in order to survive.
Putting that burden on society is "socialism" and is at odds with market economics.
You could drop the cost of care just de-regulating. But Milton Friedman failed, who would succeed today on that path?
That's a huge oversimplification and isn't true in many cases, for example when a single drug company owns the patent on a life saving drug. The laws of supply and demand are not in favor of those who require that drug to live.
Patents are a form of regulation. De-regulating would include voiding those patents. The government created that monopoly and all its attendant problems; there is absolutely no reason why it can't remove it just as easily.
We can start with the medical facilities, who will literally lose nothing by having transparency in their pricing. Now you can compare hospital prices; great!
Next we can expose the insurance companies policies per code, and we can apply them to each hospital. I could imagine tools where you select your plan, then select what you'll need.
Yes, I know there are well over 10k codes, and this can get complicated. But that doesn't mean we should just give up.
It's a start. Right now I have no idea what a hospital bill will be. If I know that I can figure out what will be left over after insurance (or even, what the cost will be when insurance company routinely denies a claim because they can.)
All progress is incremental. And pooh-poohing a small step forward is IMO what's holding us back.
Many (most?) hospitals will give you semi-accurate estimates if you hassle them long enough these days; I recently spent a month and a half and a dozen phone calls getting an accurate estimate from UCSF on a predictable medical procedure (cost: $3,300 OOP on a $10,000 negotiated rate).