Fortunately Auckland is also undertaking a massive programme of lower speed limits at present, which is a good start. And the quiet street networks of the Dutch have been well reported here before too – http://cyclingchristchurch.co.nz/2015/06/30/what-can-christchurch-learn-from-the-netherlands/ (“neighbourhood greenways” are a similar concept being used a lot in Nth America and now Chch)

Low volume, low-speed, anti-rat-run and traffic-calmed access streets are a staple of the Dutch. You do not need a safe cycleway on every street, but on collectors and corridors where cars are going faster than 30kmph. To much conflict with driveways, cars parking in and out everywhere in on-street parking. In shopping access streets, you also have pedestrians everywhere.

Remember that low-speed without all the other stuff is sub-par. When it is sub-par everyone will be frustrated and more prone to mistakes. You also need to do it everywhere (which can be done fast with these access street upgrades because of cost), so that the public more quickly (as it is cheap) can experience safe cycling for short-distances. Also so that people can safely have safe infra that links up to the more direct cycleways for moderate-distances.

There are exceptions of course, like when you want a section of an off-road cycleway to go through a access street, but you also want to continue the cycleway to not ruin the cyclists’ flow.

Further reading:

https://bicycledutch.wordpress.com/2013/08/08/making-a-1960s-street-grid-fit-for-the-21st-century/

How to prevent rat-running: https://www.youtube.com/watch?v=Okb63flApDY

Companion article: https://bicycledutch.wordpress.com/2015/12/15/how-to-prevent-rat-running/

Systematic Safety: https://www.youtube.com/watch?v=5aNtsWvNYKE