A PF in Cat 3A should have sufficient cues to assess aircraft position, flight path, and deviation from the norm – it’s the point have having visual requirements. Thus it is difficult to understand how Cat 1 or better results insufficient cues.
It might be counterintuitive to you that practise autoland above Cat I WX requires quicker reactions than Cat III autoland, but this is exactly the case, and the actual case shows us the reason why: In practise landings you have no protected zones, thus the deviation is much faster and heavier.
Of course you also need cues in a Cat III approach and must be able to disconnect or abandon the approach, but there are many more redundand systems in place to avoid such deviations. I agre that a deviation like in MUC might be possible (if for example someone violates the sensitive zone), but in real Cat III WX you can't do anything about it, you are more or less doomed or can hope you get away with it. Chances are relatively low though that something like this happens. TWR should get a warning if someone violates the sensitive zone.
So, to reiterate, yes, I strongly suggest that everyone should have relatively good WX - several 1000m visibility for a practise autoland. Autoland to relief a tired pilot is surely not intended by the inventor.