... but even just knowing the general specifications and the general time and space coordinates for their reappearance could help Starfleet respond better, saving more lives. It would be not just foolish, but actively harmful, to the Federation for original Spock to remain silent.
yes but if the specific coordinates and time are completely different from the general, they are caught in the wrong place and probably cannot do anything at all.
And also while they were sitting around waiting because they had pinned all their hopes on events repeating or at best distracted by the information, diverting maybe critical resources to that plan, they didn't think of the proper plan they should have if they were actually using their faculties on the actual data that was evident to them but was ignored.
Think of it like intelligence gathering. Yes, things may have changed since your spy reported back, or since you intercepted the message. In fact, the spy might even be lying, or the report might be a trap. But there has never been a situation where too much information has been the cause of a disaster.
There has been disaster when there has been misinformation which is what this could be. And there is a thing as too much information too, since resources and therefore opportunity is spent on information that will not contribute to the solution and may result on the critical information being missed due to wrongful prioritisation.
And the more information you have, the greater is the chance of miscommunicating it (eg Weapons of Mass Destruction).
In life and death stuggles, critical decisions and realisations can be fatally delayed or even omitted by being distracted from the reality of the situation by relying on redundant knowledge that can't reflect the situation because it happened in different circumstances. This is why starfleet expends energy on securing officers who can use intuition, because they need to be free to be perceptive to the situation on hand, not bogged down with redundent information.
Besides, who's to say the Enterprise will be around to deal with these problems to begin with? The Doomsday Machine is a great example; even if everything plays out exactly as it did before, by not warning Starfleet Spock has doomed the crew of the Constitution to death, and Matt Decker to madness. Maybe Decker, given some intelligence before the fact, could've dealt with the problem before the Enterprise even showed up, saving four hundred lives. Aren't those lives worth saving?
And maybe if Decker is given the intellegence, he fails to see another opportunity that he would have thought of if he had simply been allowed to do his job and use the abilities he demonstrated in acheiving his position: this new Decker is a product of a new timeline and therefore he will have different resources available to him. And also the encounter with the Doomsday machine is likely to happen in different circumstances as it will be met differently.
So the intellegence may have all manner of unforseen consequences, and if the solutions are limited, they could be missed. This could have a whole disasterous chain of consequences including the Constellations destruction.
Sometimes lives can be saved by inaction if you don't know what your actions might precipitate.
How do we know that in the previous timeline, that the sacrifice of the constellation prevented an even worse thing from happening? Or that the constellation could have been saved by an action that factors prevented from being revealed in the previous timeline but would be apparent due to the diffrences in this timeline if only the crew were allowed to be receptive to the actual situation?