Totally agree. Current state of Mortarboard badge is somewhat like:
I think this is something that we should think about.
There are several meta questions regarding the same ("Why is Mortarboard badge not awarded?") ..you can see some of them here, here and here too !
The current description is certainly not enough , as there is a hidden condition behind this.You cant blame someone that they haven't gone through the FAQ well since the condition may be rarely noted.
Thanks for the feature request, hope the authorities will consider this soon and we will see something like this next to Mortarboard badge:
Earned at least 200 reputation in a single day, excluding association bonus.