There is a difference simply because the results are different, whether due to the need to save face, behavior psychology, sales training, or more intangible factors.
What I'm saying is that either OP will accidentally give away information at the outset that virtually guarantees overpayment-- "Here's what I can afford"-- or robotically repeat a fair price calculated ahead of time and request TCO optimization until they are thrown out of the dealership.
It'd be like going to a shell game and requesting to pay $7 so your kid can have 10 guesses at where the shell is. Then when they ignore you, start asking what's wrong with that, I mean, those are the odds, no? I've even rounding up for that pure profit. Why wouldn't someone with a big crowd of good faith players want to accept that?
But you would have already told them, "As long as I can afford..." So they'll spend the entire exchange trying to optimize for the maximum amount they think you can afford. They can try to convince you they've optimized when they really haven't, and they can try to pick a vehicle of a lower quality and persuade you that the price drop is the optimization.
If your response to every trick is to respond, "No, please try again to optimize for TCO," they'll eventually interpret your behavior as the equivalent of an ad-blocker. Then they'll either persuade you to reveal more data or move on to a customer who negotiates on their terms.