BOAC,
Sorry if I ruffled your feathers. At the three 737 operators I have flown for it was SOP for the captain to engage autopilot A and F/O to engage autopilot B.
Student ATP commented that auto pilot A droppping out was not cool, and you responded to it by asking him why he would be using autopilot A. That was nothing to do with post number 1. I was answering your question with a perfectly reasonable answer. Alternatively he could be a captain training on a new type in which case using autopilot A would be perfectly normal.
Now two reasonable answers to your post, which was actually totally irrelevent to the original question.