We don’t say, "Visit us at http://www.askinosie.com," we just say, "askinosie.com."
It’s pretty clear that we don’t need the front matter. In fact, the latest version of most browsers are intelligent enough that you don’t have to type www in. But do we need the [dot] com part? Shouldn’t the user be smart enough to type in the brand name and expect to get the site?
The suffix is useful, and we’ll have it for a long, long time in my opinion. That’s because [dot] com uses just four characters to say, "we have a website and this is the address for it." No need to say "our website is" when you can just use four characters instead.
Toll free numbers developed a similar shorthand. We used to have to explain that an 800 number was free and that you could call it for more info. Now, the area code does all that in 3 digits.
I love the story on boingboing about how the phone company worked so hard to teach kids how to dial the phone. Everything is new, at least for a while.