Keith, the www is still there in the DNS lookup (or it would really break the system) all the browser is doing is hiding that to the user.
Hiding the actual domain is bad. I have different stuff on domain.com and www.domain.com do not make my users think they are the same, they are different domains. Might just have to ban Chrome!
I also already have a hard time getting people to just use the address bar rather than a Google search to get to the site, they're even typing the www.SITENNAME.com into Google search.
Stop trying to "Make it Easier" it is already easy, people are just lazy.