Look, this isn’t that hard. You use the “trade-in” value because you’re trading in your car. I just ran that Nissan through KBB, NADA, and Edmunds and in good condition they all give trade-in values within a few hundred bucks of $10k. That there are different prices for different transaction types does not mean that there’s some sort of conspiracy afoot, contrary to popular belief.
Yes, you could sell the car yourself and get the private party sale value, but have you ever actually done a private party transaction on a nearly-new car? I’ve dealt with it on both ends and unless it’s something that’s in unusually high demand, it’s far easier said than done. You know how long a car usually sits on a dealer lot? Well instead, it’s sitting in your driveway and you’re paying two car loans, insurance on two cars, etc. Banks will grudgingly do private party transactions, but it’s rarely the streamlined process buying a car from a dealer is. Doubly so if you’re paying off your old loan in the process, as our theoretical frequent buyers almost certainly would.
It’s all well and good that Internet Car Experts such as ourselves could theoretically get a much better deal on a short term new car purchase, but most people simply don’t have the patience. So if you must have a new car every 2-4 years, you’re pretty much stuck with trading in or leasing. Yeah, there’s wiggle room on either end depending on what kind of discount you get off the sticker or how much they want to give you on the trade in or what specific lease terms you can get, but it’s all in the same ballpark.