The precision requirements for mediump and lowp are minimums, so a computation that a shader says should be performed at mediump precision is most often actually performed at the full 32-bit precision on desktop. Overall, anything in between 32-bit precision and 16-bit precision goes. And "anything in between" is not just a theoretical consideration - mobile devices have wildly different float formats and rounding behaviors, so testing on one spec-compliant mobile device does not even guarantee that a shader will work on other spec-compliant mobile devices.
The extension does not require any support from the GL drivers, so that's why I've submitted the proposal only to the WebGL registry at this point. It can be implemented purely as a transformation of the GLSL code. If there's a strong reason for adding it also as a native extension, I have nothing against that, of course.
I'll submit an amendment to the proposal to add an enable/disable toggle. I'll make it so that the emulation is enabled by default once the extension is enabled, but can be toggled off.