Forget time travel. No sling-shotting. No Guardian of Forever. No temporal rifts to slip through.
Once again... if he lets it slip that he's from the future, unscrupulous elements could easily take advantage of him.
The only thing more I can say, is go read Engines of Destiny
by the late Gene DeWeese. It's about how wrong best intentions can go when Scott beams Kirk away right before he "dies" aboard the Enterprise-B.
Bill, the secret of Ultraviolet Radiation is not going to start a war. The secret to destroying the Doomsday Machine is is to let a damaged Starship do what it would do if Scotty didn't hold the thing together with duct tape. The solution to Tarsus IV is food.
You're desperate, it seems, to come up with reasons why Spock should not offer friendly advice regarding mundane solutions which would save untold (millions/billions of) lives.
Moreover, Spock does not have to tell everyone. He can selectively drop useful hints without giving away the secret of Red Matter.
Starfleet already knows he is from the future. Nu Spock and Nu Kirk and Nu Scotty know him as Old Spock and Old Spock is not in hiding. He is out in the open helping Vulcans resettle. Your concern about people knowing Spock is from the future is there either way.