If the Federation use Spock's knowledge of the future to its benefit, why the hell wouldn't the Klingons send their own emissary back earlier still to undo him and do even more to its own benefit. Same with the Romulans, Tholians, or Borg
Because those would create yet MORE alternate timelines, while not supplanting the original. Remember, Worf (on that DS9 ep where they meet tribbles) said that the Klingon Empire actually did try that very thing - sending temporal assault teams back in time to blow up their enemies' homeworlds. Obviously this didn't succeed in changing the regular timeline...