1. JavaScript's speed is actually not far from Mono's now. And constantly getting closer.
2. I don't think anyone but Microsoft would support .NET bytecode in the browser, simply because Microsoft controls .NET and has patents on it. It would take a lot more to reassure other browser vendors than Microsoft's existing CPs.
3. Running dynamic languages on Mono is slow. Look at the speed of all the dynamic languages on Mono (or the JVM for that matter), and compare them to native implementations of dynamic languages, in particular JavaScript and Lua. The native implementations beat dynamic languages on Mono by a large margin, simply because .NET is a bytecode made for static languages. Of course you can say that you prefer to have static languages in the browser over dynamic ones, that's a legitimate opinion of course, but not everyone would agree.
4. Standardizing on bytecode can inhibit innovation. JavaScript doesn't have a bytecode standard, which let JS engines implement very different ways of running it (V8 doesn't have a bytecode interpreter at all, for example). Of course standardizing on syntax also inhibits innovation, just in other ways, it isn't clear which is better.
5. Static languages compiled to JavaScript (that is, that use JavaScript as their 'assembly') are getting quite fast. Some benchmarks I ran found them to be around 5X slower (on the development versions of SpiderMonkey and V8) than gcc -O3, compared to Mono which is 2.5X slower, http://syntensity.blogspot.com/2011/06/emscripten-13.html
6. There is already Silverlight/Moonlight which does .NET in browsers, and it hasn't been very successful. (Of course it is a chicken and egg thing, if it were bundled in browsers it might be more popular. But the failure of Silverlight is a disincentive to add Mono to browsers nonetheless.)
For all these reasons, I don't think Mono has much of a chance to be included in browsers. Most of the same arguments apply to other static-language bytecodes like NaCl.