Cash talks. But, sometimes low priced cars are already marked as low as they will go.
I was a curbside dealer for a dozen years selling cheap cars. When I started, I left room to haggle but after a few years I changed my philosophy. I went with LOW prices from the get go and no dickering. While it dissuaded a few people, most realized my price was already better than they would get elsewhere.
Only when a car did not sell for 2.5-3+ months would I lower the price.
I have no idea what you are talking about with looking at a $4000 car and financing a $20k one. A new car dealer will want to sell you a more expensive car IF you qualify but if you want a $4000 car, you should not be going to a dealer, you should find a private party.
Negotiation involves understanding why they are selling and having cash in hand.
If a dealer has a $2500 car priced at $4000 and he comes off $1000, you did not win. You need to worry about getting the best car for your money and that is not going to be a dealer...unless you happen to find a guy like me, a one man curbstoner just trying to make a living selling a good car at a good price.
(Ive been retired for 15+ years)