highway=alleywould have been, and would still be, a good idea. It shouldn’t be a massive problem if that’s actually represented in the database ashighway=service, service=alley, because any halfway competent router/renderer will already be parsing theservice=values anyway.
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highway=servicewithservice=alleyis not wrong but potentially a little ambiguous. An “alley” can be a narrow residential street like this. But it can also be a back-access to shops and houses, not really meant as a general-use thoroughfare but as a shared service route.
I share the findings of your assessment and am willing to create a proposal for highway=alley (in a couple of days when I returned from traveling), but I also see some potential conflict/confusion with these different types of alleys (back access and narrow streets).