fnord
In the movie Uhura observes aloud: “we’re in an alternate reality!” That’s how the two Spocks can meet and interact and alternate future Spock as well as future Nero can, and do change just about everything. Except, they really aren’t changing anything, because they’re in a different reality as well as time, so whatever they do, is more or less what was destined to happen in that new reality.
In the Star Trek universe, you can travel around within your own time stream, in which case you should be careful about screwing up your own timeline (unless that’s specifically what you’re intending on doing), or you can travel to alternate realities and do whatever you want there because it has no effect on your home reality. What the latest movie did was combine time travel with an alternate reality.
To my mind, the original ST universe is intact, and Sisko and Janeway and everyone else is still there in their reality, but we’re not going to be following their stories anymore. Instead, we’ve followed Spock into this alternate reality.
Of course, the Spock we know wouldn’t just sit down and take this. He’d whip up a method of getting back to his own reality. Or would he? I don’t know. He’s an old man, and all his human friends are dead. Maybe it’s easier for him to settle in, in this alterante reality where all his friends are still alive.
One way that it might make some sense is if you throw out the alternate-futures structure and make it so that for every time the present changes, Future-Spock remembers the future differently (and if the present changes in such a way as to make it impossible for Spock to have gone back in time, Future-Spock vanishes out of the present.)
If that were the case, then meeting his past self might continually change his timeline so much that Future-Spock would be unable to process the feedback loop and could collapse into unconsciousness or worse.
I would imagine that Spock-Prime would focus his attention on helping the Vulcan people and preserving their culture. I’m guessing but I woulld think that only Kirk and Spock know who he really is. Telling anyone else or Star Fleet command would cause problems. He has scientific knowledge 100 or so years ahead of them, but sharing it could disrupt the balance of power in the Galaxy. Who knows what would happen then if New-Kirk and Starfleet had Next Generation and beyond technology.
Because history isn’t littered with time travellers from the future. So we know it won’t be invented.
Untrue…you see I came from the year 2311 in order to find the perfect chili recipe. The method of making it was lost in the Galactic War of 2199 when the Gamilons planet bombed the earth…oops, I’ve said too much.
See Rule #1, previously mentioned above…
I daresay the destruction of Vulcan has already ensured a healthy amount of disruption.
Besides, of course newKirk will have technology better than NextGen. NextGen was, like, in the eighties, man.
levdrakon said:
Perhaps I misunderstand you, but I don’t see “Destiny”, i.e. some force controlling what happens. (Okay, it is scripted, but I’m talking in story. 
) Rather, each character is taking actions and making decisions based upon the new circumstances in which he finds himself. Sure, Spock Prime is trying to make a certain arrangement work out, but note he has to take actions to ensure it rather than just let it occur.
As for the alternate reality explanation, it is only one concept of cosmology - admittedly the current popular one. A different cosmology has there being one worldline that is playing out, and things in your past have already occurred so can’t be changed. Any effort to change them is doomed to failure, not because of some guiding hand making things work out a certain way, just the fact that they’ve already occurred so whatever your intent to change something, you already failed. But that’s not what Star Trek is using.
I can’t think of a reason why inherently meeting yourself would be disasterous, but as chrisk points out, under some cosmologies the past is mutable - it can be changed. Therefore, it is conceivable you could take action to prevent your later being around to perform the time travel. That, of course, is the root of the grandfather paradox. You go back in time and kill your own grandfather (accidentally, presumably). But you killed him before he had any children. Oops, now your father doesn’t exist, so you don’t exist, so then what? Do you poof disappear? But then how were you there to kill the guy? You never lived, so you couldn’t time travel, so then your grandfather lived – that’s the paradox. Alternate realities allow that paradox to exist and there to be two (or however many) realities that play out independently but interconnect with that one causality loop. My previously mentioned single reality cosmology can’t have the paradox - you would never be able to succeed in killing your own grandfather.
As far as the OP, there is no reason in Star Trek that a person cannot interact with himself from a different point in his own timeline via time travel. The trick is that if you found yourself the older copy and didn’t remember the meeting, it probably would be a good idea to not identify yourself to your younger copy just on principle. Whereas if some older person walked up and said he was you from the future, then when you later found a time travel device, you would be fine to talk to yourself again.
From that Time Travel link by the OP:
Dr. Who had an interesting bit on this in “Blink”. It’s one of the few episodes where he interacts with someone after time travel. I’ll spoiler, because it is a plot point of the episode, and I’m giving a fair amount of detail for the situation.
After being sent back in time by aliens and separated from his TARDIS, he leaves a message for someone to discover in the future to take action to rescue him in the past. The message is left on a DVD, as half a conversation. He records his parts of the conversation real time, then years later the other person interacts with the recorded conversation exactly as if it were live. How? Someone present in the second conversation writes a transcript as it occurs, and at some subsequent point, the heroine meets The Doctor on some random adventure before he travels to the timespace point where he got separated from the TARDIS, and she presents him with a copy of the transcript, so when he is stuck in the past, he portrays his part of the conversation from the transcript in response to her unscripted responses that are written in front of him. 
From “Blink”: "“People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint, it’s more like a big ball of wibbly-wobbly, timey-wimey… stuff.”
This quote has given its name to a TV Tropes page on the often-contradictory ways in which writers deal with time-travel paradoxes.
Dude, that’s just mean!
Funny, though.