Princes Street, Cook Street and Marlborough Street are the archetype of  what we use highway=pedestrian for. They are pedestrian streets. There are many metres wide, they are flanked by buildings and they are accessible to pedestrians. They literally have "street" in their names. On the ground, they are signed with a white disc inside a red circular border. Many of these roads did, by the way, previously carry vehicles, but that is immaterial to their status as _pedestrian_ streets. Likewise raised kerbs, a red herring. Go to some Italian old towns with narrow streets and see how many of those have separate footpaths. As to highway=footway, this is a valid tagging. It can be used for footpaths that run alongside roads (often above raised kerbs) or through green areas. It can even be appropriate for very narrow alleyways between buildings. You'll see this tagging documented on the wiki, and you'll see that at least one of the sample images resembles the streets I've described: https://wiki.openstreetmap.org/wiki/Tag%3Ahighway%3Dpedestrian