I completely agree with you; This kind of thing is best saved until after the main game is assembled, if you decide to do anything along these lines. It's absolutely fine if you feel uncertain whether or not it's worth it, depending on how popular the game will be. I only mention it because as a fan of this, I feel it would be disengenuous to not voice up any concerns.
I could try listing more games with more examples, but to be honest, I think the list I've given says about as much as it's going to say, at least in terms of unlockable rewards. But I think I'd like to add a more general observation about this stuff.
Thinking back to some of my favourite games ever, they were some of the most tightly self-contained single player experiences ever made, because of one reason or another. But above all, just about every one of them have one distinct thing in common; An experience on a dedicated console, without any kind of intention of tying things to the internet. Something that was solely focussed on keeping your hands on that controller (Or keyboard), and immersing you as much as possible. That's what a lot of older consoles have over today's stuff; They don't need the internet to access a single thing in the games. That can benefit the whole thing, right down to how each individual room feels. I still remember actually feeling the cold through most of Metal Gear Solid (psx), but the warm temperature of my room gave me the impression of being in the sneaking suit. Was exactly the same for Phendrana Drifts in Metroid Prime, as well as a lot of Super Metroid (Y'know, the red caverns & that famous music, and the way you go further down through damp tunnels to get to Norfair or Maridia? Or the start of Zebes? Or the corridor that leads you to the Torian Lift? Good stuff!).
But because this isn't for a dedicated, older console; The most recent example I can think of has got to be Hyper Light Drifter, an awesome but brutally hard game on Steam. It's purely concerned with keeping you in the game, exploring everything there is to offer. It has little interest in having people poke around in the gamefiles, doesn't care that YouTube & forums are a thing, and proves that it's still possible to take this kind of approach on today's platforms (Digital distribution, etc). I'd recommend checking it out if you ever have the time. It's well & truly worth it, and the behind-the-scenes story is really interesting.
... Anyway, I know there's not much you can do about the whole internet thing (I mean... Well... Yeah), but I'm hoping you get what I mean about the game being more immersive when it's self-contained. If you get any idea on how to use that principle in your own way, there's no limit to the kind of atmosphere you can create with this. That & it helps the whole 'Keeping the player hooked' angle.
Gotta say, feels kinda good to share that bit of info with a dev. Whether it's any use or not, it's a strong belief I've had for years.