A. That's a good question, Ben. Some tech advice is so common that no one really stops to think about where it came from. In this case, there really is a reason to leave your modem unplugged.
Your modem - and most of your tech gear - contains capacitors. These hold a charge for at least 10 seconds after the power is off. Most people wait 30 seconds or more to make sure the capacitors discharge completely.
While there's a charge, your gadget's RAM is still active. That means whatever problem you're trying to fix isn't wiped out. If you plug the gadget in right away, the problem just comes back.
So, while it may seem weird or unnecessary, you should always wait after you unplug.