homecoming, arrive at, lead to, result in
歸 centers on returning to a place or state: coming home, arriving at a destination, or leading to a result. The idea of a homecoming extends naturally to outcomes that things ultimately arrive at.
歸 is the traditional form of 帰. It combines 止 (foot/stop) and 帚 (broom) with a complex left element, suggesting a woman with a broom returning home, though the exact historical development is uncertain.
The right side 帚 looks like a broom, and the left side suggests movement. Picture sweeping your way back home, arriving at the doorstep after a long journey.
For キ, imagine a key turning in the lock as you return home: key -> キ, and the door opens to your homecoming.