Frankly, the last time Spock traveled between timelines, it required the destruction of a star and a *lot* of WMDs to do it. Surely some combination of cosmic forces were at play. For him to repeat the process, even in an unpopulated solar system, would be tricky, dangerous, and probably devastating (even if he made it back anyway), which could have untold effects on the region.
Besides the type and scale of destructive energy needed, as King pointed out, there's still work to be done in the JJ verse anyway. "The needs of the many" blah de blah blah.