Right now, there is no time travel Genie in the new timeline. No one yet knows about the Guardian of Forever, no one knows about the slingshot maneuver outside of Spock. He has no ship and no capital to barter with outside of his knowledge of the future. And he's an old man.
Sounds like someone that could easily get taken advantage of if unscrupulous elements learned what he knows. You saw how easily Nero got the Red Matter from him.
I can come up with story reason after story reason why he would be reluctant to muck about in the timeline. It's not an white elephant.