For a while now, Mobile Safari has been doing something similar, although I do think in that case, it's about saving space. On Mobile Safari, the scheme is hidden until you tap the URL field to edit. The developer version of Google Chrome takes this a step further, and omits the scheme completely. Bug reports were filed, and in true internet fashion, discussion ensued.
A few things need to be made clear about Chrome's implementation of this feature. The first thing that jumped into my mind was this: some applications, whether they be web or real ones, actually require you to add the scheme (for instance, to autoparse URLs). Google claims to have solved this issue by adding the scheme to your clipboard when you copy and paste URLs from the URL field, however, this behaviour is currently broken in many clipboard implementations. Another thing that you should be wondering about now is what they do with other schemes like ftp, https,
and gopher. The solution here is decidedly simple: those will still be shown.
The reason behind this change is obvious: the URL scheme bears little meaning to most people using a browser - they know it's there and how to type it, but it doesn't indicate anything to them. Since computing has been about abstracting away complexity for a while now, it was only a matter of time before browser makers started removing this piece of web history.
That being said, I'm not at all in agreement with the "solution" Google is presenting here. Hiding complexity is not a solution - it's just hiding something. It's like Mac OS X hiding away the UNIX file system layout madness with a layer of kid-friendly directories; it only makes things look pretty - it doesn't actually solve the underlying problem. You can cover up that pile of mangled corpses in your bedroom with a flower-patterned table cloth, but that doesn't actually address the problem of there being a pile of mangled corpses in your bedroom.
Since 99.999% of the people only ever encounter http://, ftp://, and https:// (did I forget any?), why not create a standard set of easy-to-understand icons to replace them, in cooperation with other browser makers? I mean, if Mozilla and Microsoft can agree on the RSS icon (2005, people, that's how far back my OSNews memory goes!), surely we can all get along and do something similar here? Most browsers show a lock icon anyway when browsing to an https site, so this shouldn't be too big of a deal, right?