First off let me state that I am a fan of having a single, malleable timeline. From a drama standpoint it is just more satisfying that everything that was and everything that will ever be is at stake in a time travel tale.
Second, you have to work from the assumption that the older Spock as depicted in this film isn't from the Prime timeline and is from a timeline where him and Jim Kirk didn't flaunt the timeline at will. It just doesn't make sense any other way. The man let his Mother die decades earlier why precisely? My Mom died when I was ten and there isn't a day that goes by that I don't wish for a way to fix it (and I'm 38). Why would he leave that burden for his younger self to carry if he has all this knowledge of ways to change the past? Exactly what good is it going to do Spock-2 to have his mother and his people stripped away from him? Does Spock Prime see this as necessary for his younger self? If he does it is one hell of a price to pay to rectify some flaw he sees in his younger self.
Third, it would be unlike Jim Kirk not to start digging around what Spock Prime knows about restoring the natural order of things. He's practically lived a life that he was never meant to live based on meddling from the future. and if time travel and changing the past can be accomplished once... who's to say it can't be accomplished a second time?
Problem: GRANDFATHER PARADOX. This means that Spock remembering different events that cannot be corrected is impossible in a linear timeline. Cause and effect can NOT be ignored, dispite wishful thinking/assertions otherwise.