If I walk into a car dealer, lay down my cash and refuse to sign their EULA, would they really refuse to accept my money? Is an industry that's hard-hit by the bad economy going to put additional impediments in the way of sales?
Also, requiring this kind of EULA would be bad publicity for companies since it would emphasize to potential buyers that the seller is afraid of being sued for defective products. Companies that don't require such an agreement would be at a competitive advantage since they'd project an image of higher quality and more respect for the customer.
A warranty is the manufacturer's bet that the car won't die within the terms of the warranty. The longer the warranty, the stronger the bet, presumably because the manufacturer knows how good its processes and results are.
I would see such a EULA as a negative warranty, the manufacturer betting against itself. I would walk.
Many consumer contracts in the U.S. (for example those for my credit card and my mobile phone) do require binding arbitration. Why doesn't your argument apply to them?
Don't most of those contracts specify the arbitrator, too? I know I've read many articles about forum-shopping by corporations; are they just relying on the consumer to not know which arbitration forums are truly neutral?