It’s been done. Emacs, for example, has rx notation. From the manual:

    35.3.3 The ‘rx’ Structured Regexp Notation
    ------------------------------------------
    
    As an alternative to the string-based syntax, Emacs provides the
    structured ‘rx’ notation based on Lisp S-expressions.  This notation is
    usually easier to read, write and maintain than regexp strings, and can
    be indented and commented freely.  It requires a conversion into string
    form since that is what regexp functions expect, but that conversion
    typically takes place during byte-compilation rather than when the Lisp
    code using the regexp is run.
    
       Here is an ‘rx’ regexp(1) that matches a block comment in the C
    programming language:
    
         (rx "/*"                    ; Initial /*
             (zero-or-more
              (or (not "*")          ;  Either non-*,
                  (seq "*"           ;  or * followed by
                       (not "/"))))  ;     non-/
             (one-or-more "*")       ; At least one star,
             "/")                    ; and the final /
    
    or, using shorter synonyms and written more compactly,
    
         (rx "/*"
             (* (| (not "*")
                   (: "*" (not "/"))))
             (+ "*") "/")
    
    In conventional string syntax, it would be written
    
         "/\\*\\(?:[^*]\\|\\*[^/]\\)*\\*+/"

Of course, it does have one disadvantage. As the manual says:

       The ‘rx’ notation is mainly useful in Lisp code; it cannot be used in
    most interactive situations where a regexp is requested, such as when
    running ‘query-replace-regexp’ or in variable customization.

Raku also has advanced the state of the art considerably.