While somewhat a bad form for general web browsing, its definitely possible for www.site.com and site.com to be entirely different hosts. In newer versions of Chrome, you would never know which one you were actually on unless you select in the address bar.

Maybe dropping the protocol definition in the URL is debatable, as probably 99.99% of the time in Chrome a user is going to be either http or https, but dropping a part of the hostname is unacceptable in my book.

Would dropping .com be acceptable? All a user wants to see is that they went to Google, to an average user the .com could be seen as redundant clutter as well. Might as well have the address bar show "google" or "cnn" or "facebook" in it, as clearly that's what a user cares about.