Not really, you could very well imagine private hospitals bidding against each other to win a contract on providing ER services. With penalties if capacity or quality suffers by objective standards. (Isn't this how most government contracts work)

It's not like there is any competition right now? You can't even get a price quote for elective surgery.

Also I wouldn't be so sure that your children don't have significant leverage over you, hehe :) (They probably don't realize how much leverage they have)