This is a very clean and straightforward website - no BS to wade through, no popups asking for my email, just straightforward here's-how-you-do-it. If I had seen this a couple months ago I would have definitely saved a couple thousand bucks.
One thing that's really inspiring about this is that it has the potential to completely change the concept of used car sales. Just like how realtors take you around to go see houses that are for sale, a car salesman can become a person who takes you around to test drive cars for sale.
I might be wrong about your target market, but it seems like it is currently a market of wealthy individuals with high-valued cars to sell but no time to sell them. However, the quickest sales are the ones for lower valued cars - way back when I only had four figures in the bank, my only requirement for my used car was that it not make weird noises.
One lucrative direction you could go with this in the future is adding financing options, so someone could lease a used car from you and you could pass a percentage of the monthly car payments on to the car owner. Or, you could buy the car from the owner and lease it out to potential owners. I have no idea what the legal requirements are to be able to do this, but if it works you'd have a pretty stable source of recurring income.
Overall it's a great idea, I wish you the best of luck with this!