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?