My other thoughts here would be that the dealer has to make money on both your trade and the new vehicle. If they can't they won't trade. Normally I won't waste my time with a trade because I can generally sell it myself for at least 10% more than a dealer can give me. The last time I traded a vehicle with a dealer was 1978. I think people trade because they don't like dealing with the unwashed masses to sell a vehicle, certainly not for everyone. There's a sea of perspective buyers out there that absolutely won't buy a used vehicle from a dealer.
But in favor of a trade, there is less sales tax to be paid on the purchase. In this state the tax is almost 10% so depending on the vehicle sales price it could be thousands of dollars.
These are very strange times to be shopping for vehicles. The sales people pounce on anyone with a newer vehicle wanting to work a trade. Happened to me about a month ago. They were waiting for me when I drove on the lot. Probably going through the service records and appointment times.