[1] Unless you have some reason to believe the insurance is priced too low.
Insurance is usually provided by a regulated entity and implicitly backed by the government in the even that the insurer fails. Their regulators also provide redress for consumers against unfair treatment without the need to resort to the courts and the terms usually have to be fair too.
Warranties are typically provided by the vendor who may well be financially unsound and willing to treat a customer less fairly, contain significant legal loopholes and require redress through the courts or perhaps a binding arbitration tribunal.
And most machines probably do work for many years, just not sufficiently enough to offer a longer warranty. Which is fine for most homes, since you're not running a mission critical operation and a few days to pick out a new washer isn't going to kill you. A business that needs machines to work might find it worth shelling out more for a quality product that rarely quits or can be fixed on site.
No one stops a manufacturer from offering a product with a 5 year warranty, and in fact they do. Shop for products made for businesses and you will find 5 year warranties. However, they cost much more, and consumers are choosing not to pay more for the products with 5 year warranties, and instead choosing to go with the 1 year warranty.
Miele was known for making very durable products, however, even they over the years had to acknowledge that consumers were opting to purchase cheaper products from competitors, so they had to do the same to stay in business.