I think something like this would be very interesting. (Perl 6 pseudo-code, obviously)
In other words, if the sandbox is secure enough, one could use the Parrot Compiler Toolkit to write a set of bindings to allow you to write your client-side in any language you like, include bespoke languages, if desired. I think this could be a very compelling feature. Don't like languages available for client side browsing? Fine, write your own with the Parrot Compiler Toolkit and if the browser sees an unknown grammar from a safe authority, it downloads it. Otherwise, it can prompt you with the authority information, depending on your security setup.
There was a plugin for IE a long time ago allowing people to turn on PerlScript in the browser.
The DOM was the same so it didn't feel different than JavaScript, however doing it limited you to a very small number of browsers.
It never caught on.
More promising would be something allowing you to compile some subset of Perl 6 to JavaScript. The issue is how big a subset that would be. (Eval is likely to be tricky...)