Of course, this is all assuming that they even type the address in, rather then searching.
'amazon' for www.amazon.com
Firefox is generally smart enough to take me to where I want to go. The only issue is when some hack site games it's way to the top of a search result for something else, but I've only run into that a few times.
Which is itself an issue -- since many browsers are now turning the 'address bar' into a combo search+address bar, novice users may not even realize what the difference is (or was).
Try this link: http://www.news.ycombinator.com for example - this is what happens to most addresses not prefixed with www. This means that hiding the www. would mean waiting to work out that the site doesn't exist (or the connection is down) before trying the non www. version, and worse that you would get the wrong site if www.foo.com and foo.com were distinct. Hiding the http:// doesn't have such massive implementation issues.
I think people should learn about the http prefix anyway. Even our grandmas. To do that, the best we can do is to let it appear in the url bar.