What use is the shotgun for the heavy?

Solution 1:

You need a shotgun when you can't use you primary weapon because it's either slow or slows you down. This can happen in several situations:

• If you suddenly engage in a close-range fight. If you start spinning your gun, it's possible you'll be dead very soon.
• If you need to get somewhere fast and you still need to shoot on the way.
• To use a crit from K.G.B.
• If your main gun is out of ammo. That also happens.

The sandvich is a great thing, but it won't help you when you are out of ammo or if you need to fight in tight spots. I usually run with the sandvich, but I can't deny that shotgun is very helpful in some cases.

Solution 2:

Spy checking while moving. As I run from the back to the front (when an engineer hasn't built a tele) I use my shotty to spy check the usual spots, without slowing me down.

As Powerlord points out, it's also useful when you inevitably run out of ammo.