You won't be writing code in the browser anymore. Otherwise you'd have fragmentation where the user doesn't have the proper interpreter installed, and a never ending stream of "language downloads" which might be cool to devs but horribly impractical for end users.
Because we're not writing in the browser anymore, we'd be back to offline compilation and static code generation. I suppose it'd be possible to JIT the bytecode (assuming that current Javascript optimizers work on the IR; I don't know enough to qualify this any further). From my casual browsing of LtU, it seems that tracing JITs in particular may offer optimizations dificult to achieve with static bytecode compilation, particularly in identifying hot spots. But the more I think of it, that's a non-issue because you're still compiling to bytecode and JITing from there.
This feels very Java-ish to me. If you really want to script the browser in another language, compiling to Javascript (a'la GWT) would essentially do the same thing.