Incidentally, there’s also a more recent proposal for a cycleway:hierarchy=* key that would be quite similar to the proposed importance=* key, but tagged on individual cycleways. As with highway classification, a renderer could use these functional classifications to show and hide cycleways independently of official network designations.
This would probably be more useful to the cyclist who wants to get from point A to point B with a minimum of fuss than to the cyclist who is committed to clinching a demanding long-distance route, wherever it takes them. Neither functional classifications nor official designations are inherently better or worse; neither approach is guaranteed to be more or less verifiable on the ground.
Unfortunately, the proposal is a bit confusing, since it seems to be proposing two conflicting sets of keywords simultaneously. And, once again, hikers and equestrians are afterthoughts. Still, cycleway:hierarchy=* would fill a gap that neither network=*cn nor cycle_network=* serves well.