I would welcome the opportunity to wear a fedora. Unfortunately, I work in a manufacturing area, and most of the dress is business casual.
One thing that many are missing on this thread is that a little formality can breed better manners. When you wear a hat, there are some standards of respect. You take the hat off when entering a building or room; you take the hat off in a hospital, or during a church service, and certainly during the playing of the National Anthem. Of course, many people have lost this sense of manners, as you see them all the time at sporting events and parades, wearing their ball caps when the Star-Spangled Banner is played.
Formality in dress requires you to care about your clothing, and how you look. Not in a metrosexual way, but in a thoughtful way. A way that shows you respect whom you're doing business with enough to present yourself in a professional way.
And looking professional doesn't have to mean being uncomfortable. A tailored shirt and pants, a properly-knotted tie, and a jacket that is hemmed properly doesn't restrict your motions or your thoughts. It can bring about a certain level of respect however, in that people dealing with you--especially people whom you've never met before--may take you a lot more serious in more formal dress than they would if you were in torn jeans and a t-shirt.
I'll agree with you except to say that there should be different standards for those who work in IT. A good 60-80% of people in IT are social misfits or downright anti-social. What constitutes "professional" for them does not involve interacting with other people at all.
They spend 90% of their time TOTALLY away from other people, staring at a computer screen. To an IT person, the standards are reversed: slovenly appearance, messy desks, coffee cups everywhere, are signs of the tortured, introverted genius within. (And I ought to know)...
A "properly-knotted tie" always restricts blood flow to your brain, and jackets in hot weather are ridicuously uncomfortable (particularly when you are in a hurry). You can be well dressed without wearing unhealthy, outmoded clothing.
Have you seen the Sopranos episode where Tony "counsels" the young guy who wears a ball cap in a restaurant?