Should you tip a valet when it is mandatory at a hotel or restaurant?
The simple answer is yes.
Shades of green
The real answer is more complicated and is not black and white. Or in this case, green and off white. First, I try to avoid places where it is mandatory. If you look around, you can probably find some form of parking nearby. It may still cost you but it'll probably be much less. If you are on a date, pay the valet and tip. If it is bad weather, pay the valet and tip.
Quick Tip: Valet workers probably know the area pretty well and won't shine you on. If you have any questions, they may be able to answer them and you can save tipping the concierge later.
I don't really like strangers in my car. I always have personal things laying around, various gadgets and outdoor survival equipment, or maybe some emergency cash tucked somewhere. If you don't expect to have to give up your car, you are suddenly rushing to gather everything up or you just risk it disappearing to temptation. These days, you don't know for sure if any service person at any level is about to lose their home or is on a drug habit down the yellow brick road to meth city. Valet services and the establishment usually deny any responsibility for lost or stolen items just like a self serve parking lot by a dark alley. As long as the weather is not terrible, I like to walk and will find some other place to park or another place to visit.
So much of the travel business has the mentality that the more you pay for something, you more you can be skimmed all the way back to the poor house. The more expensive the place, the more you'll pay for side dishes, extras, newspapers, and attendants of all kinds. Even in the bathroom. I sometimes wish that if you are paying four times as much for something, you'd get some extras for free. If someone inherited the money, it's probably no big deal and they are not reading this post anyway. If you worked from your bootstraps to a higher cost of living, you'll probably be annoyed and not return to the place. If you are traveling on the company dime and just expense it, you are just taking the money away from your own future raise or benefits.
Quick Tip: If the hotel is in a city of any size, is located downtown or costs more than $150 a night, call and ask about parking. Don't rely on my own website here or any other big box site for the information. I say it when I know of it, but most businesses try to avoid telling you ahead of time. I get misinformation even when I ask a direct question.
Never stiff service people who you think will ever serve you again.
This is just smart practice. Whether it's your health at a restaurant or your car, it's best to pay up early. You may not recognize them but a stiffed worker will remember you and you may not want them serving you soup two weeks later.
Working for the man
The valet workers are doing their jobs and trying to make a living so it is proper to tip them when you get the car back. At least you are putting the cash back into the local economy and not up a corporate ladder. I wouldn't tip for them to park it unless you just want to try and get better service.
If you are in and out and will be using the service multiple times, I treat it like when I drink at a bar. I tip more on the first round. The staff then usually pays attention you a bit more. They will remember you and treat you better than someone who stiffs them right away. Then the tipping declines on subsequent times. That's my way of being cheap.
How about with a rental car?
It depends on what your insurance is with it and if your are completely covered for scratches and dents. How much is the risk worth to you?
Avoiding the issue and making it simple
Park somewhere else and walk or use public transportation. How about you? What do you do or recommend to others? Any bad experiences or opinions?