auto-pilot controlled landings ... I believe this is practicable now, just not deemed advisable for the public's feeling of security

many landings are on auto-pilot as I understand it, they just don't talk about it much. Certainly the old Trident airplanes (circa 20 years ago?) were the only ones able to land in fog at London, precisely because it was automatic. There is a story that the program had to be changed because it landed too flat, pefectly safe but the customers felt safer with the nose high.

From google - I just had to check my memory:
first fully automated commercial landing was made by a BEA Trident 1 in May 1967