Here's one more shot with fix for that bug that was already there that Eli mentioned.
Now if the user has set search-default-mode to t and if they do C-s, the description is still "" (not "regexp "). So the minibuffer would read "I-search: ".
Below is the patch created using git format-patch with appropriate commit log.
From df1a6e8e9d8227f5c137236a09fda9818c479d0c Mon Sep 17 00:00:00 2001