In a way, using GLES2.0 is much nicer and more streamlined than "desktop GL 2.x".
Also, until very recently GLES2.0 had a "conformance tests" suite to check implementations for conformance, whereas desktop GL did not. Desktop GL only got the conformance suite about right now (siggraph 2013), starting with OpenGL 4.4.
He didn't like it that much.
If you're not porting OpenGL 1.x software (and thus not using APIs long considered deprecated/to avoid) there's no big issue with OpenGL ES as far as I know.
ES is supported on mobile phones and tablets, like Android and IOS, where people would obviously like browser support. If they used full OpenGL, they would lose out on those markets.
Not exactly true, AFAIK, OpenGL 4.1 was the first "full" OpenGL version which was fully API-compatible with ES (2.0, you need OpenGL 4.3 for ES 3.0 API-compatibility).
IIRC, none of the OpenGL versions prior to 4.1 were complete supersets of OpenGL ES.
What I see now are the great failures of OpenGL ES. Having to specify line widths in the shader. Inconsistent support for points. Not being able to predict if a shader will have one instruction too many and fall off the fast path. I've learned it to great depths but the mental pollution I had to absorb in the process has caused lasting damage in the form of resentment and exhaustion.
If it was up to me, I would scrap the whole thing and just give developers full DSPs so they can write their own renderer in a language like a hybrid between Go and Matlab, but with exact specifications and basic hardware guarantees.
Wasn't the fixed-function pipeline in OpenGL ES 1, and removed from 2.0 following the OpenGL 3.0 -> 3.1 transition?