About powers, the mind and the bat.
All the potential thoughts someone can have are interconnected. Thinking about one set of things leads you to thinking about something else. The thought processes that correspond to powers aren't naturally connected to anything a normal human being can think of; the bat forcefully bridges the gap.
Agnes can turn it off and use it as a (very sturdy) bat to cave heads in with when she's not giving out powers or exploding heads.

Here's a power suggestion for someone that should be running around in the background as a comic relief character that gradually becomes absurdly powerful: A guy who developed the superpower of RPG level grinding.