I agree there is an underlying ‘theme” to the various scenarios as I think they all render down to little more than a single factor. Basically “is the person currently to inspect the passport responsible for Immigration?”. If yes show them the one they want to see, if no show them the one (or both) you want them to see.
Perhaps a little more complex, given say a visa in one passport and a name that matches a booking in another, but that’s the sort of situation a canonical answer would cover.
I think generalization might help to extract the relevant considerations from an element of extraneous ones usually connected with a set of specific circumstances. Also that a few, perhaps colour-coded, diagrams would aid clarification while unlikely ever to be provided for the non-routine conditions that would have to be present for any further "two-passport" question to avoid being a duplicate.
What concerns me slightly is the we in “we create”. I have seen many good ideas proposed on metas that have not been carried through (but more on SO than TSE). I am not sure that advocating some work for someone when I don’t intend that ‘someone’ to be me is entirely appropriate.
In general, of course we want canonical answers – there should be no need to ask that! But if asking anyway is an implied request for assistance I don’t wish my agreement to imply much by way of practical support, in the matter of dual nationality.
Incidentally, I say ‘dual nationality’ rather than ‘multiple passports’ because I do not have dual nationality (hence not well qualified to help) but do have more than one passport. That raises issues but I think not ones that should be covered by the proposal above.
