The problem here is that you are financing the extended warranty as well as the purchaser of the car.
Pay for the warranty with other funds and you're fine.
One thing to beware of is that IF the original warranty from the maker is transferrable to you, the "extended" warranty does not kick in until the other warranty runs out. Count the years of coverage vs. the years of paying for it to get the true "per year" cost.
You also learn more about most extended warranties by reading what the don't cover, than you do by seeing what they will admit to covering. The worst ones are those that cover ONLY the engine and drivetrain parts that are "internal" and covered with oil, or language similar to that. The alternator, for example, is not covered by such restrictive language.
Some consumer advocates say extended warranties are a rip-off, but that is usually in the context of buying a new car, which these days has a pretty good warranty already built into the purchase price. For used cars, and for people who don't mess around with their own tools on the weekends, a *decent* warranty can make sense.
To take the current vehicle without the warranty, I would expect that the total $$$ financed would be a bit lower. If not, this is a ploy to get the same thing as a price more than what they bargained for. Rare but not unheard of.
No one is forcing you to buy THIS car. If it stinks too much, take your ball and play somewhere else...IF the contract for sale is contingent on you getting the financing approved. A shark-type car dealer will have a contract that keeps you on the hook to pay for the car even if the financing falls through. For you, the extended warranty for a used car is enough of an "essential" part of the deal, that being unable to get financing for it *could* be a way to get out of the contract.
However, it all depends on the fine print for your strict legal rights, and the dealer's commitment to customer satisfaction even to the point of losing today's sale with the hope of getting more business
from you AND your referrals later by letting you out of the deal.
IME, the hazard of cars breaking down increases more with mileage, than it does with number of years old.