If you view human beings as perfectly rational machines then dress codes make no sense, but that's not what we are. Dressing formally puts you in a different frame of mind. It reminds you that your work is serious and that different standards apply to how you act and talk than in your casual personal life. If you dress to work the way you'd show up to a dive bar, then you're that much closer to behaving like you do at a dive bar.
Economist Tyler Cowen makes another good argument for formal dress: it is a vehicle for social mobility.[1] In a society that values formal dress, you can signal your intent to move up the social hierarchy by how you dress yourself. If you want to become an elite, then dress like one and people will take you seriously. But when the elites adopt casual dress in their professional lives, what is left are much more subtle and hard-to-adopt class signifiers: manners of speaking, interests, childhood experiences, travel, etc.
Yet another problem is that dressing "smart casual" is actually more difficult and expensive than wearing a suit. A suit is a great equalizer. A $2000 suit is not all that different than a $300 suit. And you can very easily get away with having only two or three suits. But smart casual is much more difficult, subtle, and expensive to pull off.[2]
[1]http://www.businessinsider.com/wearing-casual-clothes-at-wor...
[2]http://marginalrevolution.com/marginalrevolution/2017/05/inf...