It allowed their defense to rest while putting KC's right back on the field. In theory it was logical, but it really only works if you can get a TD on that opening drive and get a 4th down stop or takeaway. A punt lets a FG win it, and a FG lets a TD win it. A stop is obviously the best case scenario, but a TD won't kill you unless KC goes for 2 (which I think they had discussed doing to avoid giving it back for the sudden death score). If they traded punts, FGs, or TD+XPs, the third possession could end the game.