Maybe I'm taking this a step too far but doesn't Gödel's Incompleteness Theorems (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...) state that a language can not define itself? You need a meta language to be able to define and specify a language in its entirety.
In other words, regex can not parse regex in its entirety. It's impossible.
Can a C program parse C source code? A Java program parse Java source code? Yes, they can, so such a general limitation couldn't be the reason regular expressions can't parse themselves.
In other words, regex can not parse regex in its entirety. It's impossible.