The reason you see the signs is probably because there's a bigger -need- for signs. People do (or did once?) go barefoot in the US more, I think.
But there are: warts, foot fungus, liability from stuff that might be on the floor, minimum dress code.
I would bet that many places have "no shoes" on the signs because that's how they're sold; I think it would be hard to find one with just "no shirts, no service" on it.
And for them it's about maintaining a dress code--not "white tie" or "no denim," but "for god's sake, be fully dressed!"
and yeah, I really react badly to the "why are Americans so ..." sorts of comments.