My parents have a concierge medicine relationship with their physician. It's fantastic. He is a complete professional who cares deeply about all of his patients (he works nights and weekends, does research outside of business hours, works around insurance and exploits every legal loophole possible to help them) but holy crap is it expensive. They are paying for their normal insurance plus this service ($3000 annually). This is what it's come to in the US---to be able to have a semblance of a relationship with your physician you need to pay a premium on top of the gouging that your "insurance" already charges you.
Note: My parents are not* rich, they scrape by on social security and my dads part time work fixing sprinkler systems.
Note: My parents are not* rich, they scrape by on social security and my dads part time work fixing sprinkler systems.