I've had a draft blog post lying around for a while where I try to explain why I think people should care about looking nice. Which is now redundant :)
There is one point that I want to add - which is that there is also a meta signal you send by how dress. As you pointed out, by dressing nicely we can get people to treat us better because we're signalling wealth, status etc, and also because people just respond better to attractiveness.
But even if you imagine that you are interacting with someone who has no feelings about clothes/attractiveness, if you dress badly you are signalling to them that you don't care about, or are unaware of, how people respond to you. You're signalling that you're someone who just leaves value lying on the table.