sorry, what I meant is, it's helpful to keep tags like route=bicycle on the individual relations too, which I see you've just added back, thanks

regarding how you would see the whole network - for most networks it's unfeasible to create a super-relation (E.g. all ATMs in NZ or all state highways), so the usual approach is a query like 
https://overpass-turbo.eu/s/1uq5 or 
https://overpass-turbo.eu/s/1uq7

in small cases like this, there's probably no harm in keeping your superrelation, as long as the individual relations still have the correct tags