Why is there no permutation in Regexes? (Even if regular languages seem to be able to do this)
The fundamental theorems of formal language theory are that regular expressions, regular grammars, deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs) all describe the same kinds of languages: namely the regular languages. The fact that we can describe these languages in so many completely different ways suggests that there's something natural and important about these languages, in the same way that the equivalence of Turing machines, the lambda calculus and all kinds of other things suggests that the computable languages are natural and important. They're not just an artifact of whatever random decisions the original discoverer made.

Suppose we add a new rule for creating regular expressions: if $R$&nbsp;is a regular expression, then $\pi(R)$ is a regular expression, and it matches every permutation of every string matched by&nbsp;$R$. So, for example, $L(\pi(abc)) = \{abc, acb, bac, bca, cab, cba\}$. The problem is that this breaks the fundamental equivalences described above.  $L\big(\pi((ab)^*))\big)$ is the language of strings that contain an equal number of $a$s and $b$s and this isn't a regular language. Compare this with, for example, adding a negation or reversal operator to regular expressions, which doesn't change the class of languages that are accepted.

So, to answer the title question, regular expressions can't do permutations and we don't add that ability because then regular expressions wouldn't match regular languages. Having said that, it's possible that "regular expressions with permutations" would also be an interesting class of languages with lots of different characterizations.