I pretty much figured we would not see eye to eye on the matterI don't think I can agree with the distinction you are making between connected and configured. Using you description of a delta connection, if I had a 240 Delta service and had a 208V, 3ph machine to install, and decided to use a 240 Delta-208/120V Wye transformer to stepdown to 208V for my machine, but only made 3 connections from the transformer to machine (120? out-of-phase relationship to each other,) I'd have a delta - delta connected transformer. I don't buy that.
I agree with your description of primary and secondary connections (in the case of an isolating transformer) but the problem, it seems to me, is that with the autotransformer one of your connections would be both primary and secondary...it is the same connection. I think this is where "primary" and "secondary" descriptions break down with autotransformers, and IMO, is why section 450.4 uses the descriptions of "input" and "output" for autotransformer, rather than primary and secondary.
My main concern is conductor protection, as 450 covers xfmr protection. What NEC sections do you see as covering conductor protection of autotransformer-connected circuits?
For the sake of discussion, let use an example of two-wire in, two-wire out... and an abnormal condition to stress my point. Let's say we have 24kVA-rated autotransformer transitioning 120V in to 240V out. Max-rated in current is 200A. Max-rated out current is 100A. What ampacity conductors do you use, in and out, and what rating is your circuit ocpd?