Paul, that's one way to look at it. I prefer to look at it thusly:
Nice enough? Do you know where Japan would be with out us, the old USofA? The smallest fucking province of the Russian empire!
Nobody has ever been as generous to defeated foes as the US has been to Germany and Japan. After the war the Russians occupied part of Germany, but we kept them out of Japan, calling their bluff to move forces in.
Without going into detail it is only in recent years that the Japanese Self Defense Forces have had the capability of truly defending the home islands. When the war ended they put everything into the economy, deciding that defense would be restricted to a relative amount based on I think one percent of GDP. By defending them with those bases we allowed their economy to grow FAR MORE than it would have otherwise, in addition to all the other preferable trade policies, artificial Korean War boom from us buying there, etc.
And if they want us to leave all they have to do really is ask. Same with the Saudis. We are there to maintain the peace in Asia, especially as the Japanese and Koreans don't always get along so well.