A lot of people use GWT for large web applications instead of JS, precisely for the reasons Dart was created, we just don't go brag about it.
The biggest problem with GWT was how slow the toolchain was, and this is adressed with Dart by having a native VM in Chrome.
Out of curiosity, do you know of any notable non-Google sites using GWT? I see a few here, though none seem to be particularly large web apps - that I can tell, at least.
Given that its supported by Sencha (ExtGWT), and Spring, and IntelliJ, you can probably guess that the vast majority of GWT users are in enterprise environments. :) AngryBirds uses GWT. You actually don't see many people writing very large Web apps outside of Google precisely because most organizations didn't have the resources to produce something like Closure or GWT. Duplicating GMail with no tooling using basic JS is quite a tall order.
Many new Google services these days use GWT, like Google Flights, Hotels, the new YouTube editor, Google Offers, etc. AdWords is written in GWT too and is quite large (millions of lines)
One of the problems Dart hopes to solve is to have a large codebase(apps easily into the millions of lines of code) that is toolable, and statically optimizable. Javascript is particularly poor at this.
The Closure Compiler was actually invented by the Google Mail and Calendar teams as a way to wrangle Javascript and tame it's suckier bits to enable sane development of large apps.
