It's been a very long time since I flew the 737, and even then it was the 3/4/500 series with no roll out capability, so this is a general observation rather than type specific.
Cat 2 & Cat 3A require a 'fail passive' auto-land system which, as you probably know, in the event of a a single system failure would require manual intervention but the aircraft will be in trim and present no handling difficulties.
Cat 3B requires a 'fail operational' auto-land system which, in the event of a a single system failure would complete the landing and roll out automatically. The manufacturer will have risk assessed the impact of a single failure below alert height, in which event it is acceptable to continue. This doesn't mean that you can't go around, indeed it may be wise to for some failures.
The A320 QRH draws clear distinctions between the equipment required for Cat 2, Cat 3A & Cat 3B approaches. I would have thought that Boeing would have done something similar.