I agree the "A0" designation doesn't exist but it is helpful when teaching people who have no experience in the military field or hobby. Saying M923, M923A1, M923A2 out loud gets tiresome and confuses them with all the numbers being spurt about not to mention all the other models of that series. I'm all for correctness for those within the hobby as we can spurt off M##A# and know exactly what we're talking about but for the common Joe they can't keep up. When I'm asked the differences between the m939 series trucks I go "There are 3 variants of the m939 series truck (or m923 if we are talking about it specifically). The base M923, which we will call the "A0" model, is blah blah blah." At the end of the comparisons I'll remind them the designation "A0" doesn't actually exist as it's just the base truck. Zero -> non-existent -> no designator.
I believe the A0P1, A1P1, etc designators are interesting and wouldn't be surprised to run across more.