Mark Kleiman has a totally non-funny story about how, yes, you need to wait to get health care in America and, consequently, he almost died. The punchline is here:
It was only later that I discovered why the insurance company was stalling; I had an option, which I didn't know I had, to avoid all the approvals by going to "Tier II," which would have meant higher co-payments. The procedure is designed to get very sick or prosperous patients to pay to jump the queue.
The insurance company almost killed a man in order to try to persuade him to buy more expensive services.