Are crossings like https://www.openstreetmap.org/node/12156384359 really crossings in any meaningful sense, because the Bing imagery shows nothing: no lowered kerb, no tactile paving, etc.
https://www.bing.com/maps?cp=51.540076%7E0.007217&lvl=22.0&mo=om.1&pi=-22.2&style=x&dir=60.8

If there are residential streets where separate sidewalks only "work" when fictitious crossings are mapped for the renderer/router, that is a good argument not to map them. For routing purposes, tagging with sidewalk=both and mapping only the real crossings as nodes should suffice.