I read a fascinating article about this once; a linguist (I think) was explaining that this habit — which much of the rest of the world scoffs at as "fakeness" — had to do with the US's vast and diverse immigration history. Smiling is a primate gesture of submissiveness. Smiling shows someone — with whom you can't communicate in words (such as because one of you is a Swede and the other is an Italian) — that you don't mean any harm, and you're non-threatening. In short, smiles are a reflection of our long history of diversity and attempt at getting along.

For that matter, personally, I think there's a lot of good in much of what the rest of the world calls "American fakeness." It's really just about a cultural belief that EVERYONE deserves basic courtesy, even if they're complete strangers or haven't "proven themselves" by earning lifelong-bestie status. In other words, in Europe, a lot of people believe that courtesy needs to be EARNED. In the US, a lot of people believe that everyone deserves basic courtesy automatically, simply by virtue of existing.