I agree the primary reason for Spock to share his knowledge would be attempting to save lives.
For him to see an incident approaching which he knows is going to cost lives but takes no action is unconscionable, IMO. I just cannot, under ANY circumstances, not see him siding with the needs of the soon to be dying if he doesn't act.
Of course there could there be negative consequences for choosing such a path but at least those consequences could then be faced and dealt with normally. What ever results occur from doing the right thing is a better result than living with the guilt and corruption of his characters integrity by not attempting to help where possible.
King Daniel wrote:
Look at what Daniels' attempt to protect Archer caused in "Shockwave" or Braxton's attempt to fix history in "Future's End". Look what happened after "Endgame" in the novelverse.
This is why I wish the Nuverse was NOT the same one as the ENT version we saw. Because that connection implies single timeline time-travel could be possible in the Nuverse and I do not want it to be so, for the very reasons you state. I want future timetravel in Trek to be remain based on the multiverse theory; from now on all timetravel leads to a different branched reality just as happened in ST. Goodbye paradoxes and reset buttons forever.
Say Spock warns Starfleet about the Borg. Starfleet investigates a century earlier than the Hansons' did in the Prime universe and try something Kirk-like and reckless which brings the collective down on an unprepared Federation. Say he warns them about the Bajoran wormhole, which leads to an earlier Federation/Cardassian war. Say he warns Deneva about the parasites, and a century later a survivor's child starts experimenting with the omega and renders the entire alpha quadrant impassable to warp ships.
I'm not saying Spock 100% shouldn't interfere, but I can see why he may choose not to.
Spock could take steps to prevent premature exposure to threats he intends to intervene in...
I'd think of it as a matter of risk. You've described risky scenarios where the payoff could be either great good or disaster on a galactic scale. So yes, it's probably not good to interfere, here.
Now if V-ger shows up at Earth's doorstep, or the whale probe does, and the threat is immediate and time is short, I could see Spock Prime saying, "I may be of some assistance, here."
Spock Prime could be like a firefighter helping put out fires when the occur, rather than the cop on the beat, trying to prevent or deter things from happening.
He could prepare a series of files on a SFH computer with the prescribed solution enclosed which will not allow access until a pre-specified stardate.
Well, Spock was the very first character to warn us of the dangers of contaminating the timeline back in 1966 with Tomorrow is Yesterday.
But that was a closed timeline where you could create causal paradoxes by killing your grandfather or breaking up mom and dad in 1955. With a branching timeline
there are no dangers to the original timeline, because you're not in it anymore - indeed the only person in the nu-Trek verse who ever was is old-Spock.
I wish we knew for sure the old TT rules are permanently retired. Nutreks connection, as mentioned above, to ENT complicates the severing by association.