DNS ... I just don't follow the logic of offering me more in trade in an attempt to get me to spend more on something else.
How can you NOT understand this? Do you think the dealer is in business, to buy things? No. The dealer is in business to sell things. Profit is made in sales, not in purchases.
It isn't about advantage. It is about business. To stay in business means making a profit. When businesses fail to make a profit, they fail.
Since you have your 2 prices and you are okay with having two prices, I don't see why you don't feel the buyer, a dealer, can't offer you two different amounts. Why do you get to have two selling prices but the dealer can't have 2 offering prices?
However, to put it into your emotional framework of what you are attached to or not, the dealer is more attached to cash than to merchandise. So your gun is worth less cash to the dealer as a cash purchase than as a trade-in. It really is that simple, especially when that cash is walking out the door and immediately reducing the dealer's financial position without any profit attained than giving you more credit for the same gun, making some immediate profit on the purchase you then make because of the trade-in.