Yeah, I agree there's definitely a dilemma between Collective Rule and the NC.
As mentioned, lots of players will just REX and war, never buidling the NC. I think this is viable in MP, but in SP on higher difficulties, larger maps, you need at least one Observatory city to get there. The beakers to get to that tech are a problem, but once it's built, the Observatory bonus = the NC bonus. Hopefully you can Academy all your Scientists there. Even so, early Science is a real problem. But all in all, it is possible to pull off with the Mayan due to their Pyramids, and still, a lot of your weight will be carried by War. So civ's that have powerhouse Renaissance UU's like Arabia can probably do this as well. The problem is that players will try to do this and not know how, when it really does require a lot of unorthodox city stagnating, some city specialization, and a very, very aggresssive posture.
The other option above is buildng the NC and only then starting the Settler spam, Worker first. I think that leaves a lot of players feeling that the opening lacked power. This opening will only have 1 or 2 cities more than a Tradition opener on T80, and the benefits of Liberty really only come on the condition that 6+ Settlers can be trained. Otherwise, most of the benefit from Liberty has to be seen as coming from Republic, Representation and the Finisher, which although underestimated, are going to be worse than Tradition a lot of the time.
One thing I have tried as the Maya, however, is opening Collective Rule and buidling a delayed NC and Observatory in my second city. I might have around 4-5 cities at this point, financing a Library in the last. It's a slightly later timing, but the Settlers definitely come out quicker from the Capital in the meantime, and then while the NC is building they travel to the square I want them to settle, furthest areas first. I'll escort them, then if any civ's happen to come with Settlers during that time I am usually ok to DoW them, picking up a free Worker. The staggered timing allows me to send Settlers to a lot of the coastal or Island locations without losing turns I'd otherwise have spent in transit. Then I get a few religion benefits on-line, connect cities for the eventual Meritocracy, and otherwise prepare for the huge happiness dip when they all settle. When the NC goes down, 3-4 cities will be planted that turn, which usually brings me to about -10 happiness as the Luxuries are getting up.
I wouldn't say this is possible a lot of the time, but some map features make it optimal. First, I want more than one 3 food tile along with plenty of hills nearby so that city 2 can get enough production early enough. Marble helps. Most importantly, I will plant this city next to a Mountain for the Observatory later on, with the intent of settling my Academies there. Also, I have to be able settle this city within 3 tiles of my capital, for the purposes of sharing Academies, or the early Manufactory from Long Count. Since 4-5 Pyramids are going strong, the Manufactory usually comes on-line about mid-way through the NC build. But definitely I want to found my Academies overlapping the Capital and city 2, so that the Cap can use the Academies before then. I might consider putting the first Academy on a sheep tile in city 2 so that Production isn't as affected by working, but I have not tried that as yet. Also, the timing could possibly be delayed into a very late NC + Observatory at around Education as well if I really have to rush military or territory. But the general principle is to make up for an early NC by compounding it with the Observatory bonus in City 2, further down the line. In that game, the Capital is the Military/Settler production powerhouse, and the second city is the Science generator.
I haven't tried it for any other civ, but I would definitely consider it for Babylon, Egypt (GL opener), Inca, and maybe France. Any civ that has good early Science, Food, or Production bonuses could pull this off, as well as any civ that's naturally good at going wide. But the main thing is that it's quite dependant on terrain. You have to have a good food location next to a Luxury and a Mountain, ideally overlapping your Capital's borders in one or more workable squares. But 3-million world age gives that often enough that I find myself trying it more and more.