The first playable module released was the hangar.
The second module was Arena Commander with 3 versions. Murray Cup Racing, Vanduul Warm / PvP and Freeflight.
The module next released was the social module, you got to explore a tiny version of ArcCorp Area 18 and say 'Hi' to other player avatars, with some scripted NPC's that mostly just stood there T-Posed.
The fourth module released was the 'Peristent' Universe (minus it's persistence!). We had Delamar, moons and planets you couldn't land on and GrimHex.
From the moment that tiny PU hit the servers the other modules were abandoned by 99% of the player base. As more and more has been added to the PU (despite some new additions like Star Marine) even more simply never bother to visit any of those other modules. If you could go back in time and tell players who only knew Arena Commander and Murray Cup Racing what they can see and do in the current game, a lot of them wouldn't believe you, they'd say you were dreaming - never gonna happen.
The modders manual will be more or less a small-scale version of a tool to make an Arena Commander type experience. As others have said above they won't have the main features 'plugged in' that make the PU a living breathing universe.. so why am I bothering to type this out now? Because there are things not mentioned above.
1. Quanta is tied into everything in the PU. NPC's, their factions their personalities and thus their behaviours. The reputation system, including player history that records your UEE Naval service in Squadron 42 will affect everything you do, and even where you can legally go and the type of work you can get in the PU. You will not see that in a private server. There will be no UEEN or Advocacy presence on a private server. The best you will get there are Skyrim type scripted NPC's with canned dialogue, unless the modders make it themselves (some can be very good - the best Skyrim V content is made by modders), but they can never be universe wide personalities.
2. The live economy. Again affected by Quanta, there will be no live economy in a private server shard. This is why you cannot transfer your character between private and live PU... even if they weren't using some exploits in the private servers. Modded servers will not have persistence the way it is planned to be in the PU.
3. A living breathing live universe. Unique mission givers, multi-part breadcrumb adventures, one-off events - daily / weekly / monthly and yearly calendar events. IAE, Invictus, Luminalia etc. there will be more to come. Politics and media personalities will be alive in the PU. You won't ever get to meet Timo Baxxi on a private server, or Jax McCleary. There will be no live Murray Cup Racing events to attend. The Arena Commander racing tracks are virtual recreations of 'real' PU Murray Cup Racing calendar tracks based in various star systems you will have to go there to attend them. you will have to put together a team to be able to enter the competition. There will be only 1 Murray Cup final Champion per year, and it will be recorded in the history of the PU, the player will have it on his personal record and even NPC's will refer to it. Players and NPC's alike who enter the MC, especially if they win races will be interviewed on the Spectrum news and sports programs.
FOIP and VOIP were not developed as a thing for players to tinker with making funny machinima videos, they made that facility to allow live in-game events to happen. Actors would sell their firstborn to get a significant role on Game of Thrones.. it will be the same thing to get an ongoing personality role in the PU, because its guaranteed work potentially for years and often they can work from home if they have decent sound recording set up. There is nothing to stop Mark Hamill signing into the PU and making an appearance in a Chairmans' Club Lounge, the game has that capability right now. They could get a group of actors to roleplay and riff off what the players and NPC's are doing - live. That is what server meshing is for, to allow mass participation in live events. No other game universe has that capability, and you insist to refer to Star Citizen as some common-all-garden MMO type thing - it is not and it was never planned to be. Drop in drop out sounds so casual doesn't it, until you realise just what you could potentially 'drop out' to.
There will be other things to do and see in the PU. The Metropolitan Opera House is on Mars. Do you think someone with a private server set up is going to employ a whole team to get a well known opera singer to attend their server version and sing to any players and NPC's who turn up? People say, how can they raise money from players after the game launches? We already know they can restrict access to certain players for certain areas, that means they can sell tickets to players for virtual in-game events... and they will. any type of experience you can think of, they can put it into the PU. No private server and it's small group of supporters could ever manage more than a tiny portion of that. Why will players never desert the PU in any significant numbers? FOMO! There will be something happening somewhere in the verse - almost everyday.
Don't discount the players and the organisations, they will have their own events and CIG will do all they can to facilitate them - The Daymar Rally will be a thing and if they want to organise a virtual BarCitizen in a bar in the game and have a karaoke contest - they can do it... and they will. The only limit is your imagination. No player, not even a developer will be able to see everything in the game in a whole lifetime because they can't be everywhere at once.
The things I mention here are not even exhaustive, there's more that we know of already. The Chairmans' Handbook talks about Fashion Week on Terra III.
4. The Spectrum. This is an often ignored part of the live universe experience, and no wonder because it isn't in the PU yet. All we know of right now are pre-scripted videos of coming events - but the Spectrum will have it's own regular scheduled programs with personalities who exist in the game universe, the Spectrum personalities will respond to events going on inside the PU - we had an election, there will be others and they will be live in the game. Players will be able to role-play news reporters in the game universe and that live service will go out to anywhere with a screen both inside the game and outside of it, MobiGlas or real world android portable device. it's why they keep going on about Spectrum, there has never been anything like it before.
The reason you have the idea that players will go off the to small hand-built private servers and desert the PU is because you just don't know the true scale of what is coming, and that is not your fault, becuase there is a whole load of information that is archived now and it takes new player and those without the time far too long to go and find it. talk about it in the Spectrum and some Negative Nancy is going to insist we are all just dreaming. Perhaps they will do it less now that they see CIG are capable of having live events inside the PU and make stories that have characters, not just mission givers, that exist in the game universe? Probably not.
Think private servers made with modding tools and level design kits, think cut down version of the Arena Commander modules... hardly anyone will bother with them, it will be a niche thing. Comparing Star Citizen to ED or NMS shows you haven't really grasped yet the scale and depth of what Star Citizen plans to be.