I see - that wouldn’t just apply to sidewalks, but address a more general question, like in your earlier example where a pedestrian street continues uninterrupted across a junction with a road.
I’m worried that making it too general would raise more questions. For example, if this is to be used for all junctions, we’d need to discuss how to tag a situation where both roads are continuous (e.g. an unmarked junction of two country lanes), or how to unambiguously specify which of two roads are continuous when both are, for example, tertiary. And a tagging scheme that’s too complicated could hinder widespread adoption.
Could your suggestion be further simplified to crossing:continuous=yes? With yes meaning that the “lesser” way is continuous and no meaning that it isn’t (the implicit default).
I like the idea of a poll by the way - we’ll have to make a decision somehow.