Hospitals, airports, and other places have added valet parking services in the last few years. I am a big fan. If the sign says "Free Valet Parking," it doesn't mean you shouldn't tip. I have seen many prosperous-looking people give the valet a big "Thank You" and drive away.
To really appreciate the valet service, you must have wandered around several floors of garage ramps and stairs in the sweltering summer heat, wondering where you parked. Try it on a walker. Try it pushing a wheelchair. Try it if you're sick of upset, or both.
My late friend Sally had rheumatoid arthritis for about 40 years, and had replaced most of her joints at least once. She still loved to travel. Her husband dropped her off at the airport curb one day. I guess he assumed that the baggage handler would push her wheelchair along with the luggage. She rolled down the ramp and turned over before anyone could help. Bleeding freely, she somehow caught the plane to Atlanta before stopping off an an ER to get patched up. A valet would have helped, but I'll bet her husband would have stiffed him.
My favorite valet was one at the cancer center where I went for regular chemo through 2009. When I left after my last visit, I told him I wouldn't be back for awhile. He said "Let's make a clean break of it, then. It never works to be just friends." Yes, I'm a good tipper.