Answer to CM's question
CM, the answer to your question is that many can, and it has been demonstrated many times. The big jets are typically tested well beyond the values shown in the AFM or FCOM to be sure they are robust, and that they exhibit no adverse behavior in the event that conditions are unexpectedly or unknowingly somewhat worse than the values published for routine use. In fact if you look closely at these AFMs and FCOMs for some types, you will note that the autoflight limitations posted clearly additionally state the qualifier "when landing minimums are based on their use". So that in many instances, where reported visibilities are reported as above Cat III minima, but actual conditions are nonetheless equivalent to Cat III, such as in a driving rainstorm, or blowing snow, or even with a landing landing into a blinding sunset with bright reflections off the runway, these AL systems are beneficially and effectively used as an aid, sometimes in wind and gust conditions even beyond the value cited above.
As to the relative performance of the AT in the latest modern big jets, have you even used those systems in stressful conditions, to be able to make a relative comparison of their performance???
Regarding your comment about RNP and ANP, you noted capability during GNSS "SA OFF" operation, during normal ops, as for a GNSS approach. But this is hardly any indication at all of the suitability of your aircraft for RNP capability, which deals with containment in normal, rare normal, and non-normal ops. So even if the equivalent of ANP or EPE for your jet on a GNSS straight in approach was reasonable, that in no way addresses or assures its LNAV and VNAV ability to deal with RNP containment or useful RNP capability, especially at the lower RNP values down to RNP .1. It also says nothing of the overall AFDS and related system's ability to safely fly the necessary paths for departure, for RNP based RF Legs during approach, or for RNP paths on an E/O MAP approach initiated from the TDZ. To do so, the FMS/FMS and related systems like the redundant IRUs, standby electrical system, AP and FD, and map displays, in combination need to be demonstrated to be capable to achieve the specified robust normal, rare-normal, as well as non-normal performance, in designated conditions, including having adequate FTE for all the designated control modes to be used. In short, to date, there is no evidence so far that the jet you mention has or can demonstrate any of this, even for RNP procedures that have now been in beneficial and safe use globally now, dating back to before 1994. Perhaps you could jumpseat on a flight someday in a real RNP capable aircraft, into NZQN, PAJN, or CYLW or equivalent, and see this RNP capability used first hand, to better see how much more significant capability other jets now have, and why AT performance alone is only a limited part of an overall aircraft's operational capability, regardless of how good the AT might be? Which is just one more reason why this Vapp thread is quite important and significant, to those who are legitimately trying to understand and deal with these important questions and issues.