Why should an insurance company that signed up 10 customers get the same price as one that signed up 100,000? Because health care is fundamentally incompatible with free market capitalism (information asymmetry is extreme, demand curves are whacked, and there's often no competition due to time constraints) so allowing this sort of thing just leads to monopolies.
To put it another way, they should receive the same discount because if they don't, the smaller insurance company will go out of business and we'll ultimately be left with a few gigantic ones who use their market position to simultaneously squeeze hospitals and customers.
Aren't there single-payer systems where medical care is still private, and the government pays them for services? I doubt those systems would put up with "we'll tell you how much you have to pay when we're done" so I'm sure there are examples to follow.
> Mandate a final, guaranteed, all-inclusive price
How would that work for something like birth? Depending on the amount of time spent in labor and a host of potential complications (some requiring presence of additional doctors like anesthesiologists or surgeons to perform a C-section) the costs will vary greatly.
> require disclosing every single discount made available to anybody, or even require charging the same price to everybody
That could work, as long as discounts don't evolve into kickbacks or rebates, but then why should an insurance company that signed up 10 customers receive the same discount as an insurance company that sent 100,000 people? The latter loses their leverage, which typically sends the prices up, not down.