I tend to stick with Immortal and I've never actually accomplished the whole 4 city & NC by turn 80 as I always find something else I want that delays it.
Personally I don't see the issue with holding off on the NC so long as your cities keep growing & you have enough workers to improve tiles.
Building Oracle first means you get your free aqueducts and growth bonus earlier (if you are finishing tradition) and pops a Great Scientist earlier for a better academy.
Diety is much less forgiving and many players seem to ignore early wonders completely, which in this case focusing entirely on growth, 4 cities and the NC is advisable. But again it depends on your circumstances, if on Immortal/Diety you spawn next to Shaka you should go straight for construction and get composite bowmen adap and forget the NC until your position is secure.