The numbered node system predates broad internet access and still provides paper maps:
https://www.holland-cycling.com/index.php/tips-and-info/finding-your-way/numbered-cycle-network
Important nodes may include their own public maps to help direct people on the smaller details at towns. One thing overlooked in many other countries is making the route continuous, it needs clear direction at every junction of paths/roads to guide people between the main nodes without getting lost part way there.

Sorry, and one more comment. I think a certain amount of pre-planning might be inevitable. If I want to go from Halswell to Kairaki (which is almost possible on the current network and will be in a short while), it would be odd to find signage for Kairaki in Halswell. The problem is that it is the nature of a network that not all possible destinations can be signed everywhere. Of course, if I know my way around I can make it up as I go along and think “follow the signs to the CBD, then go to Papanui, then at some point branch off the parallel on to the CNC to Kaiapoi, then go through the town to hit up with the Pegasus Beach trail” (in which case I would have missed the Nor’west Arc alternative that will be build soon). But I could also pre-plan my route and just memorise three or four numbers, or look at a map that would ideally be located at least at the nodes themselves to memorise the nodes.

Point taken about the signs. There are other examples (e.g. the North Rhine-Westphalian design http://odenthal-altenberg.de/fileadmin/_processed_/7/e/csm_knotenpunktsystem_def09ff300.jpg) where the signs include both the name of the nearest destination as well as the node (and sometimes, as seen in the picture, also the names of trails of which they form part). I personally like the design where the node numbers are part of the main sign rather than add-ons, which is why I picked the photo that appears in the article but the destination name can easily form part. In my experience using a node network, pre-planning isn’t necessary to use it if you take a map with you or there are maps along the road that include the nodes.

Using a connected network on the ground shouldn’t require the use of apps or preplanning. Good signage is vital.

I don’t think the Inland Scenic Route should be called a safe cycle route between Rangiora and Winchester/Temuka. I can’t even work out which road is being used between Geraldine and Temuka. That route has many single lane bridges, blind corners and hills. Rakaia River causes issues which ever way you approach it. While there are stretches of SH1 where there is plenty of space to add an off road cycleway I don’t see much point without the Rakaia link being added.

On a positive note I look forward to seeing the rest of the new cycleway between Rolleston and Templeton along Jones Road completed. The small section that has been completed looks great but doesn’t yet link to anything.