The point is not to initiate operations but to deter operations, e.g. China or N. Korea attacking Japan. China will not engage us, and they won't risk it by attacking a direct ally with our forces nearby.
There is no deterrence as the Chinese know that the 32,000 US troops in South Korea cannot be used to deter them.
So why waste the money?
Putting our troops in new bases on the west coast of Japan would do FAR more to discourage China (as we could use them to respond to anything the Chinese would do). Not to mention that the Japanese government has been looking (for some time now) for ways to move some of the US military presence off of Okinawa onto mainland Japan.
It would kill three birds with one stone; creating a real deterrence against China, easing the US military presence on Okinawa (which is a big headache for Tokyo), and it would still position our troops for a rapid reaction to any situation on the Korean peninsula.
All we'd need to do is pre-position our military equipment in the southern part of South Korea, away from any North Korean artillery bombardment. A quick ferryboat ride later, and an instant army division, ready to go. Assuming that the South Koreans did their job in maintaining the equipment.