I doubt you'd get a very good, highly detailed game running at 60fps with WebGL and asm.js today. Nothing comparable to what you'd get running well on a console. Maybe in another couple of years, but not today, and by then we might have non-web platforms doing 4K 60fps with ease.
But a lot of games do run quite well using WebGL. Just not the jaw-droppingly realistic ones.
you can, you know WebGL is hardware accelerated and there is Asm.js - even the Unreal game engine runs in Firefox and Chrome.