Dart: a huge improvement over JS. Browser requirement: no worries.
I have been writing some code in Dart to replace code I had previously written in JS. I am quite pleased with how much better the software-development process has been and the readability and maintainability of my Dart code (compared to JS). Simply put: JS is rubbish compared to Dart.
The class-based OOP is very nice and so easy for me to apply my Delphi, C#, and Java experience to, and the google-provided APIs for maps, lists, string manipulation, async operations, and so forth have cut my development time and lines-of-custom-code way down. The strong-typing (or pseudo-strong typing) in Dart is fantastic for preventing common errors too. Generics: wonderful to have. Inheritance in a non-prototypical manner: priceless. Resulting code is just so much easier for anyone to work with.
Sure, Google may not be able to get others to adopt the Dart VM in their browser, but I do not see that as an issue. This is not the "old days" where many of us faced rather limited hard-drive space or RAM (or even processing power). I figure if I write a web-based application in Dart, I can require my user-base to install Dartium if needed, since it it just an "app" (the browser that is... the browser IS the app that runs my app). It is not any big deal to have Chrome and/or Firefox and/or Dartium installed (dare I say, and/or IE?). Fact is, many people have multiple browsers on their machines already and are quite comfortable being forced to use one or another. So, if you need a browser with a Dart-VM installed in order to run an application/site you want to use, so be it. What's the difference between that or requiring your users to have OpenGL-capable graphics card to play a particular game, etc? For this reason, I do not see Google having a showstopper condition for Dart just because other browsers do not use their engine.