I don't see it.
I'm a fan of old Spock mostly keeping his mouth shut but even if he spills out everything, it's a big galaxy and many many unknowns are out there.
Turn left instead of right to avoid the Doomsday Machine and walk right into the Whatever Device you wouldn't have otherwise found.
But the scope of known space in the TOS timeframe is limited; if the Enterprise crew of the new universe did avoid the Doomsday Machine and encountered this other threat, the problem is still there, as it would still have been encountered in the original timeline, and Spock Prime would still know about it. For example, say the next movie opens with an extradimensional rift opening up in Federation space and releasing a horde of vicious monsters into the galaxy, the Feds could simply go to Spock Prime and ask him how to defeat them, as he's obviously from the future and would know what steps to take, and the crisis would be solved. Also, the USS Enterprise's mission to "seek out new life and new civilization" and "boldly go where no one has gone before" would be unneccessary, as Spock Prime would be able to tell them exactly what was out there.
That is, IF he decides to tell them anything.
But you make Spock sound as some kind of all knowing entity.
Just because Spock is from the future, it does not mean he knows every detail, every mission, every action taken and every threat that was encountered by every starship out there during his lifetime in the Prime Universe.
I also do not believe that for many situations things are really as straightforward as : Problem emerges ---> Spock gives solution based on future knowledge ---> Starfleet applies solution --->Problem solved.
Sure for some situations it could be but very often even the best and smartest battle plan does not survive contact with the enemy.
It often took many steps and events in certain sequences to occur for situations to be resolved happily. Who is to say trying to apply the final solution from the start will succeed and not cause unforeseeable problems ?
And in the end, who is Spock to start playing god with the galaxy ?
Saving for example the new universe Romulans from annihilation by the Hobus supernova might seem like a good thing and a great diplomatic move. Billions are saved.
Only to have Romulans decades later maybe start another war with the Feds, killing millions that would have lived otherwise if nature had done its job.
As for the to "seek out new life and new civilization" and "boldly go where no one has gone before" mission, it is hardly unnecessary.
How much knowledge does Spock really have about everything ?
Knowing about the Gorn and where they are or knowing a summary of their history is nothing compared to having to go out there and meet them and interact with them.
So they have spoilers and some knowledge on paper and in a computer.
They still have to boldly go and it is where noone has gone before.
We do know what is in Saturn or Jupiter.
Would it make it any less an achievement, any less magnificent or wondrous to go there ourselves for the first time ?
Not in my opinion.