It's definitely not simple, but I'm confident that it can be done. For something like birth, you'd have a baseline, then extras for various contingencies.
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.
