You make me wonder which assembly you're talking about. x86-64 feels heavy with legacy designs, many ways to get the same result, common pitfalls regarding memory management, and some surprising very specific gems to make some things fast… such as SIMD.
I'm just talking about design goals - the original assembly was introduced so that people wouldn't have to remember the numeric instructions of the processor. The instruction sets have been legacy even before that, with slight improvements occasionally, but at least the target audience was people in the beginning. With asm.js the target has been compilers to begin with. With most assembly dialects the instructions have a clear purpose, where as with asm.js you have arcane rules on what makes what stay as an integer, etc., enough so that I think most of the group of sane people would prefer writing against traditional assembly dialects than asm.js.
Maybe that's a good thing, at least then the goal is that people who care about performance don't write JS. But I'd prefer to just have the compile target as numbers then since you can't read the result anyway.
(I know little about other instruction sets.)