I think I've got a piece of inducted reasoning for what the guru adds, actually. This will... be a bit weird, so bear with me.
For 1 blue eyed person, it's easy. You don't know anything about how many blue eyed people there are on the island until the guru tells you.
For 2 blue eyed people, it's still quite simple. You already know there's a blue eyed person on the island, but you
don't know that person 2 knows there is until the guru says so. That's the crucial piece of information the guru provides.
For 3 blue eyed people, it's harder. You already know there's a blue eyed person, and you know that person 2 knows there's a blue eyed person. However, you
don't know that person 2 knows that person 3 knows that there is until the guru says so (think about it - if you theoretically had brown eyes, person 2 is put in the same situation as the example above, and doesn't have that information). This is the crucial piece of information the guru provides.
For 4 blue eyed people... the same again. You know there's a blue eyed person, you know that person 2 knows there's a blue eyed person, you know that person 2 knows that person 3 knows there's a blue eyed person, but you
don't know that person 2 knows that person 3 knows that person 4 knows there's a blue eyed person. This is the crucial piece of information the guru provides.
This can be extended all the way up to 100 blue eyed people. Sure, you know there's a blue eyed person, but you don't know that person 2 knows that person 3 knows that...
The guru doesn't really add any information beyond the N=1 case. But the islanders, being Vulcans, refuse to use strategies that aren't completely based on logic.
It's nothing to do with that. Assuming no communcation is possible, there really is no way for them to work out their eye colours without the announcement.