ITA. I think that the US West coast & seaside cities are pretty different than much of the US in that it's much more acceptable to be dressed casually. I find that oftentimes you have to be dressed nicely or at least have some type of recognizable handbag to guarantee good service. I'm not saying that you won't have good service if you don't, but the chances are lower.I would say it depends on where I am. I live in LA, so no, I never dress up to go shopping here and not many locals do. I think I was wearing flip flops last time I was in BalLA and the SAs greeted me and were super friendly.
But when I'm in Dallas or New York (and most places in Europe) I dress a little better because that's the culture. I'm not saying I get dressed up just to shop, but in general people don't dress as casually in other places as they do in LA. In some cases, it's easier to look nice than get no customer service, which can happen.