Recently I've got a custom request from one of my top customers, which asked on how to enable Captcha for search for anonymous users.
There is a very simple solution for that. Modify code for bb_plugins.php and at the place where it lists $cond1, $cond2, $cond3... add below the following:
$cond4=($user_id==0 and $action=='search' and !isset($_GET['loc']));
The final condition should list the following:
if($cond1 or $cond2 or $cond3 or $cond4) $enableCaptcha=TRUE;
It's a question of why actually would be needed to enable Captcha for search. I personally think it's not a question of instant bulking or attacking the site calling the search algorithm (any server should have a protection against such kind of primitive flood; Apache has it for sure).
I could suspect this is done because forum owners are carrying about the protection of their data, which is "automatically stolen and classified" through the search mechanism.
I would be more than happy if somebody writes a program, which steals the data from miniBB forums - why not? All references are kept anyway. But you probably need to be more than a legend before somebody will even try to do so ;-)