The problem with US healthcare: childbirth

We just got a >$22,000 bill from the hospital for the birth.

The services provided:
1) A private delivery room for about 2-3 hours
2) A shared recovery room for about 36 hours
3) shared nurse service for the duration of the stay
4) some baby diapers, a water bottle, a baby outfit
5) meals

The charges don't include the services of a midwife, hearing test or the pediatrician.

The insurance company negotiated rate for this was around $3200, and our cost was another order of magnitude lower. We have this wonderful system where charges are nearly an order of magnitude greater than what is really "paid". The main "advantage" of insurance companies is that you get a real rate, instead of this sky-high rate. (Perhaps they are hoping to catch un-aware PPO patients. If a PPO paid 70% of the charges at a non-participating provider, the patient could be on the hook for over $6000 - assuming the insurance company even considered the rest to be reasonable and customary.)

Why don't hospitals actually charged the $3000 rate to normal people to everyone, instead of playing this game with insurance companies?

Even this reduced insurance company rate seems extreme.
An alternative to get the same cost (though with a much higher quality of service):
1) Two nights in a high-end luxury hotel: $1000.
2) Six meals at high-end ultra-luxury restaurants: $600
3) Private nurse: $1500
4) Very nice supplies: $100

Good luck getting the insurance company to pay for that.

A home birth would not have any of these hospital expenses. The charges for the home-birth midwife would likely be similar to the hospital midwife. Thus, the overall charges would be much cheaper than the hospital birth. However, since the "insurance" plan doesn't cover homebirths, the patient would have to pay for everything out of pocket. Thus the "cheaper" homebirth costs much more than the "expensive" hospital birth.

Don't you love the US system?