Since Don Grady left the show after season 11, why did his name still show up on the credits of every episode of S12 when he did not star in any of these last season episodes?

We've discussed this several times, maybe we can provide a link -- SteveA on this board located a short video showing the correct, original Season 12 opening.

What you are seeing commonly is an incorrect opening that was spliced onto Season 12 prints decades ago. Grady's name did not originally appear on S12 episodes.

Yes, this is the opener that was provided for showings on Channel 7 in Australia. It doesn't include Grady:

https://www.youtube.com/watch?v=TbuJEHoIAhU

Thanks for the info, Biff and Steve. I hadn't seen that before. But that explains it!