That will largely depend on what kind of company he's representing. If it's a new market start-up or even an established company like Microsoft or Apple, then you're right, but if it's a more traditional corporation like e.g. a bank or an insurance company a more formal dress code will still apply. The "don't wear brown to town" dress code may be less rigid in the city nowadays than it used to be, but it has not disappeared alltogether and is not likely to do so in the foreseeable future.
The thing is, though, that the modern U.S. Banker, dressed in a business suit and tie, is still less formal than a Banker would have dressed one hundred or so years ago (in full "morning dress", which looks a lot like what many would consider ultra-formal these days, i.e. a tuxedo with tails).
It's quite possible that this trend will continue into the future. But, if it does, it could easily mean that, yes, Bankers can wear polo shirts and slacks, but everyone else is wearing tank tops and shorts.
The other problem is that, yes, one person in power (or just in celebrity) can influence fashion in this way, but if so then it's just as easy for another person who comes later to influence it the other way. If we elect David Crosby to the White House in 1972, the next guy will start wearing a tuxedo in order to distance himself from his predecessor.
http://www.hatsrcool.com/blog/?p=662
Must've been the last POTUS to wear a topper, surely?
You know, that reminded me of something else. My parents used to say that the reason people stopped wearing hats in the '50's and '60's, at least from where they came from, is because people were stealing them when you leave them in the coat room at the restaurant. Don't know if that's true or not, but it would be an interesting way to get rid of jackets as well...