I heard some American friend that it's part of American culture to control climate: drinks must be piping hot in winter and full of ice cubes in summer. Everyone has to look like they are in a hurry and everything has to be BIG. Combine these things and to-go insulated cups become a cultural phenomenon.
Then again it's funny that in Western Europe alcoholic drinks to go are totally a thing and people love drinking beer on a lawn when it's nice outside. Again, cultural differences...
EDIT: I was thinking mostly about Italy, France, Spain, Benelux, but Austria has a pretty solid café culture too.