The physics engine is difficult. I want to go with only the asm.js physics engine, but at the time the asm.js version was built it lacked the ability to disable collisions. That's pretty much the only reason it's not the default, since right now any project using that feature will be broken by switching across to asm.js.
Adding that feature to the asm.js build has become very complicated since Emscripten subsequently got a bunch of updates and broke backwards compatibility. So despite the asm.js physics being open source, it's no longer useful since it does not build with Emscripten any more. I contacted the original developer on a couple of occasions, and they say they are too busy to update it. Besides people are now asking for features like certain types of joints that aren't supported by the (now fairly old) version of box2d that the asm.js version was built against. So to get that one last feature for asm.js and make it the default, the entire asm.js port of box2d needs to basically be rewritten from scratch. That is a pretty complicated project, and the end result may not even be backwards compatible with what we have now either (even just a slight change in the way floating point calculations are rounded can have a cascade effect with results like a tower of objects falling in a different direction with significant change to the gameplay).
Since as ever we get a constant stream of feature requests and we could never have time to deal with them all, we prioritise the easy ones, or the really important ones. This is not easy, and I see the existing situation as acceptable (there is the high-performance option with a single missing feature, or the slower box2dweb which has collision disabling). So weighing it up with the amount of work vs. benefit to be gained, I see it as not ranking very high. That doesn't mean we won't do it, it's just more likely to fall behind other things (like the requests we get for the image editor, and 'open external editor' is a good example of something easy which can bring a lot of benefit).
Box2d and Emscripten are both free open source projects, so in theory anyone could come along and do this work, and then we should easily be able to integrate it back in to the behavior. But with all the other demands other customers are making it's hard to justify ourselves doing that. So if you know how to do it yourself or have any other developers handy, building the latest Box2D with Emscripten and writing the bindings is 90% of the job.
I don't know what tests you guys are running but asm.js typically comes out 3-4x faster than box2dweb for me. I just ran another stress test to confirm: 2700 objects at 30 FPS with asm.js, and 850 at 30 FPS with box2dweb, making asm.js over 3x faster, and that's in Chrome which doesn't yet specifically compile asm.js code like Firefox does.