Japan is a prosperous country. If the bases closed down, it's not as if anyone would starve. Most likely the JSDF would either take it over, thereby continuing the revenue to local businesses. or the area would be opened ip to residential/industrial development. And as for Japan's neighbors, which ones are you reffering to (that are hostile)? China's elite class is prospering too much by capitalism to consider war. They've learned the lesson from America and will build a financial empire rather than a military one. I think it's safe to say that China has no interest in provoking a conflict with Japan because of the economic consequences. Their respective heads of state have recently made mutual visits and promised good relations.
The JSDF does not have the funding, or the need, for the base. Besides, this ignores the other bases; the Navy has basing facilities on Honshu still that the Japanese want us to keep (hell they were upset when we stopped basing a CVBG), because right now Aegis and the SM-2 Block IV LEAP is the best defense against North Korea losing it (sanity breaking out there is not a given, after all, it hasn't yet) and launching a nuclear missile, or a barrage of chemical or biological missiles, their way they've got. (It is no accident the JMSDF bought Arleigh Burkes, and they've been trying to get their hands on the LEAPs since it was on the drawing board, but the technology is not up for export by law.)
China has a huge standing military and they have demonstrated a willingness to provoke international incidents that could escalate to war. The country is unstable and may yet, like Germany before it, decide to solve their severe internal problems and indefensible borders via the strategic offense. China also has outstanding (and honestly quite legitimate) grievences against Japan dating back to WWII, and they've been pushing those internally even as they reach out the hand of friendship externally. It's not as clearcut as you make it sound. So far the Chinese have made a point of keeping their options open in the "we might decide you look good invaded" department.
Plus removing basing from Japan would greatly hinder the ability to protect Taiwan if China decides to make something of that.
There are similar cases. Closing down Diego Garcia in the Indian Ocean would remove a major stablizing influence on all the powers there. India has made noises about harassing their neighbors, like Pakistan, before. Iran is not exactly the friendliest of nations. There are a lot of smaller nations on the eastern edge of the IO that do not get along, too, but know that it would be looked on unkindly if they were to start something in an area of major shipping lanes.