Cat 3A with fail passive and still only need 75m midpoint (EU-OPS)
Absolutely NOT, you need 125 for the MID. It's not a matter of control loss but a system redundancy. CAT III Single on FMA (airbus) automatically means you're fail passive hence 125 M RVR requirement, mind you the autopilot is still ON. you can check the tables for RVR requirements for auto rollout.
So I return once again to the question of why no Cat 3A DH ?
The answer is lightning system installed for CAT III A and B. Obviously CAT III A doesn't require such a extensive lightning network as CAT III B, main difference is taxi routings and apron along with SMGCS whereas the RWY's lightning is almost the same. Operational benefit is obvious then ,isn't it? CAT III A can be flown with AH logically being fail operational and autoland being compulsory. Conclusion one can land without visual reference on CAT III A airport. The restriction of being fail operational, of course, alienate the possibility of manual rollout yet a min RVR must be in place. It's not directly related to rollout redundancy in this case but rather a matter of emergency services reach-out in time. Mixture between CAT III A airdrome and fail operational capabilities of aircraft created new set of rules.
P.S. AC 120-28D, is an extensive reference. FAA includes the option of fail operational for landing and fail passive for rollout which isn't available on airbus at least.