An observation is that 'or-max' cannot currently be defined by the user, because there is no way to expand rx forms explicitly. One way to fill that hole is to add the function

  (rx-expand-definitions RX-FORM)

which would expand RX-FORM until it no longer is a user-defined form.
This would permit or-max to be defined as

(rx-define or-max (&rest forms)
  (eval `(regexp ,(regexp-opt (or-max-strings (list forms))))))

(defun or-max-strings (args)
  (mapcan (lambda (item)
            (pcase item
              ((pred stringp) (list item))
              (`(or-max . ,rest) (or-max-strings rest))
              (_ (error "Illegal `or-max' argument: %S" item))))
          (mapcar #'rx-expand-definitions args)))

Of course, if the 'or-max' operator is generally useful, it would probably still make sense to define it as a primitive.