As my college RA who suffered from an extreme fear of zombies once told us during one of his multiple zombie preparedness meetings:

Never try lighting zombies on fire, especially if you’re in the same building as them. You know what’s the only thing worse than a bunch of zombies shambling up the stairs towards you? A bunch of zombies on fire shambling up the stairs towards you.

You underestimate our ability to analyze every problem and solution, and then light both of them on fire.