We do in some sense but we call it something else like 45x120 or similar. That's not 2x4" but nor is a 2x4 actually 2 inches by 4 inches generally.
But what we definitely don't do is stick build homes using 2x4s apart from interior walls. An exterior wall where I live would probably use 45x220mm studs and probably more wood as well for a total depth of 350+ mm.
Realize we have a very, very large country, and it's chock full of forest, so plenty of lumber resources to do such things. Other places use different materials/techniques/etc which are mostly based on what resources they have easy (read: cheap) access to.
Also not all of the US uses timber framing, for instance, in costal florida, it's not uncommon to have concrete walls that are framed with sheerwall inside, so they can survive a hurricane.
