Of course, you should never sell the car to the dealer and should always make the effort to sell private party, which will often get you 50% or more greater than the dealers best offer.
But here is another consideration. Sales tax. If I buy a car and trade one in, the sale price that I pay taxes on is the price of the vehicle I am buying minus the trade in.
For instance, if I buy a new car for $30,000 and trade in a vehicle and they give me $15k for it, I pay sales tax only on $15k. That saves me about $1k in my area in sales tax. If I could have sold the used car for over $16k, then I would technically be money ahead. But your time is also worth something. For it to be worth it to me, I would need to be able to get at least $17k for the used vehicle to make it worth the effort.
Then on top of that after COVID dealer gave me $5k tradein for an Ecoboost car with a leaking cylinder wall, check engine light, missing parts, etc. where KBB was less than that. I really don't get it.
It’s really not a lot of work and if $2000+ for a few hours work is pitiful, I envy your financial position. List on Craigslist at bottom market prices (you’ll still come out way ahead of the dealer), aggressively filter out tire kickers, sell it within 3-4 showings.
The law is very favorable to people being allowed to sell their personal vehicle without jumping through additional regulatory hoops.
Americans really get extremely stupid when car related anything comes up.