FWIW, at least in the U.S. the consensus appears to be that they are in fact access=private, and that receiving deliveries and taxis is an implicit “individual permission”: Help needed: review of road access restrictions (mostly Massachusetts) - #7 by ezekielf
(Personally I disagree with that interpretation and agree with yours but it looks like we have a large hill to climb)
Zooming out a bit, I think tagging access on a short, dead-end driveway is pointless: first of all it’s obvious from it being a short dead-end driveway, and second of all it doesn’t matter. Just leave it untagged.