Beginning-of-line or indentation on one key

mbol-advice.el

(defun my/mbol-advice (arg)
  "With prefix ARG other than 1, return t.
Else, go `back-to-indentation', and if point hasn't moved, return t."
  (if (eq arg 1)
      (let ((start (point)))
        (back-to-indentation)
        (eq start (point)))
    t))

(advice-add 'move-beginning-of-line :before-while 'my/mbol-advice)

Updated so that if a prefix argument other than 1 is passed, move-beginning-of-line will be immediately called using the prefix argument, since back-to-indentation doesn't use a prefix argument.