I do it, or come very close... I have a saving account set up that I put 'car payments' in to, which does nothing but sit there and collect interest. When I'm ready to buy a new car, I've paid for it in advance, and have the money ready to go. Meanwhile, instead of doing car payments on the new car, I continue putting into that account.
It really isn't a matter of having cash on hand, its just pre-paying for your car and keeping the interest, vs paying after the purchase and paying someone else. And you don't have to be well off to do it, you just need to keep your current car for 2x as long as your current loan term. (ie, you have a 3 year loan, at the end of 3 years just pay 3 more years into the savings account. Your next vehicle will be paid for!)
(important part bolded! If you go through cars quicker than 2x your loan payment term, you are going to cost yourself money!)