I've never really felt the NC-first was a hard and fast great opener. It's an amazing opener when the situation is right, but the build/tech order is far from rigid and there are a lot of situations where it simply doesn't make sense. I think a lot of the people who uniformly denounce NC-first haven't done the build in a situation where it makes sense yet.
If the world is small, or if you have a really close rival, or if you're in a starting location that really sucks to defend, NC-first is awful. There's just no way around it. But if you can settle on Marble (and thus get access to it instantly), the world is big, you're on your own private peninsula or island, or you have a city-state between you and your closest rival (bonus points if it's Militaristic), the early NC starts looking a lot more attractive.
Even when it is attractive, there's a lot of other things to consider. Is it worth going for Calendar first to try to slam out Stonehenge before Writing comes along? The early Culture boost helps a lot, allowing you to snag Aristocracy and a few other policies from Tradition early to help supercharge your rapid-expansion phase.
Do you attempt to grab the Great Library the instant after you get your NC? You can snag Civil Service for free this way, which will get you out of the Classical era VERY early and set you up to benefit greatly from being a city-state patron.
Stealing a worker is also a big decision, since you could use the extra hammers to spit out a couple warriors. However, a convenient worker is not always available, and even if you do find one there's no guarantee it'll be close enough to the work you need in time.
Generally speaking I'd say that early NC is a good setup to have in your back pocket if it becomes obvious in the first 10-20 turns that it'd be appropriate, but starting the game with the express intent of running early NC is asking for trouble.