This is a good point, I hadn’t thought of that. When a path doesn’t have access tags then in Scotland it implies foot, horse, bicycle = yes (and there is no difference between highway=footway and highway=path in this respect) but not all routers may realise that, so it can’t hurt to add it.
Still I’m not sure how many people would use that approach. I just feels wrong to tag, for example, the CMD arete with bicycle=yes just because you would technically be “allowed” to ride a bike up there.
In practice, from looking at the tags on the paths when I’ve been hillwalking, I think at least some people in Scotland use bicycle=no to map where it’s impractical or impossible to cycle even if it isn’t illegal (example 1, 2, 3). It’s technically wrong but it has the same effect, it prevents bicycle routers from sending anyone up there. It’s shorthand for a combination of surface, smoothness, mtb:scale, sac_scale, trail_visibility and others tags which would indicate that you wouldn’t want to ride a bike there, especially a road bike. It’s an easy “mistake” to make because it mirrors how wheelchair=yes/no is used.
I guess at some point these could all be surveyed and re-tagged, but doing that without adding all these other tags could have unintended consequences…