In other words, by doing Aiki Toho Iai, you aren't now doing Aikikai Foundation weapons or the Aikikai does not now have Iaido a part of it's official curriculum.
Honestly, Have Hombu dojo EVER had Iaido
as part of it's official curriculum? I don't think even Nishio Sensei said so. Aikido is aikido. Iaido is iaido. Within the 4 walls of Aikikai Hombu dojo they have, as far as I know, never
included Iaido kata as part of their grading curricula. Saito would teach Sunday classes where he often taught suburi, 31 kata and some paired kata (kumijo and kumitachi). I believe both 2:nd Doshu and Tohei sensei sometimes led outdoor training in jokata (Similar to 31/22 kata).
Neither 2:nd nor 3:rd Doshu have, AFAIK, ever forbidden any aikiken or aikijo training as part of any particular shihan's curricula. It was just never part of the formal curricula of Hombu dojo, i.e. with respect to examination requirements etc.