I've also seen snow tires perform worse than all-season tires, e.g: https://www.tyrereviews.com/Tyre/Michelin/CrossClimate-2.htm vs https://www.tyrereviews.com/Tyre/Barum/Polaris-5.htm

If tires complying with the standards overlap, then the standards are meaningless. When there's requirements for snow tires, but not for X brand or model of snow tire, than it's not doing any good. That's why it's important to have a snow rating that can apply to tires of any type, and if it meets that rating, regardless of the rating for dry warm weather, than it should be good to go, otherwise not.