One issue is control.

With a weapon, you're trying to hit a highly mobile opponent in a vulnerable spot. How are you going to do that with a sword dangling off your wrist by a chain? If you're lucky, you won't hit yourself in the face. Or, if it's really heavy, your foot. Even if you're still carrying it around, what good does it do you if you can't swing it properly?

With a shield you're probably not all that bothered if it *does* hit you in the face -- better the shield than that spiked ball on the other side of it. Plus, the shield is bigger and just keeping it near your vulnerable spots is a decent (if not stellar) way to use it.