Stainless steel is used for practical considerations, getting a sufficiently effective container for a reasonable cost.
Regardless what material would be ideal, you still have to turn the raw materials into your end product. Stainless steel is a material easy to fabricate with, and its corrosion resistance makes it suitable for many ordinary liquids, such as food and beverage. It also makes the resulting product durable.
Dewar flasks have been made from other materials, including glass, ceramics, plastics etc. If you were building a space probe or a sensitive medical instrument, it would probably be worth the extra cost to use more exotic materials with more challenging fabrication. But if you're trying to build something to sell for $9.99 at a local retailer to store coffee in, those other materials aren't worth the hassle.
Plus, stainless steel isn't all that great of a thermal conductor anyway. I have a stainless steel saucepan with a stainless, uninsulated handle. I can have it on the stove boiling water in it, and I can grab it by the handle barehanded and the handle barely feels warm. Copper comparatively is about 25 times more thermally conductive, aluminum about 10 times.