South Korea needs China because getting closer to them is the only way to reunification. The US has no leverage over North Korea, China does.
Partially, yes. The other reason is economic necessity, the South Korean economy is very close to China, not just for trade, and also, as I said, if China offers to 'help out' rebuilding the north, the economic ties get even closer.
Why on earth would the "tribute system" be a reason.
Not a reason as such, however Korea was a tributary state of China until the end of the Joseon period. I'm not suggesting that there would be a 21st Century return to this, there wouldn't, but for historical reasons, I really think that the Korean people would be more comfortable with a close relationship with China than the US and certainly Japan. The Ming came to Korea's aid in the Imjin War and the PRC intervened on behalf of the North in the Korean War. Having Chinese help rebuild the north could go a long way in winning over the support of the newly united-Korean population there, as would close ties with China.
Well there's already a lobby in the States who want America to dramatically reduce the size of their military bases in Japan, if not remove them altogether - they figure it costs too much for too little return. So they'd be all in favour of more rearmament - bigger Japanese military means less need for American bases...
The Americans are
already solidly in favour of Japanese rearmament. There is a large push to get Abe to increase Japanese military spending and take over a lot of what the US forces do in the region. Essentially, you could argue that it's a move by the US to get Japan to act as its proxy in the region, so there can be wars, but with minimal risk to the US / US forces.
...in this scenario I doubt those lobbyists will get any support if the US is forced to withdraw from Korea...but knowledge of the existence of those people plus the American withdrawal from Korea just adds further support for the right.
Why? The only reason the US states for its presence in the Korean peninsula is to support South Korea and help protect against the North. With the North removed, I'm pretty sure that South Korea will be very quick to politely thank the US for its help, then politely ask it to remove its bases.
Also, the major reason for US forces remaining in Japan is to protect Japan against existential threats. During the Cold War, this was the USSR and China, now it's North Korea and China. With the North Korean threat removed and an expanding military, Japan can quite effectively fight against China. The US does not want to get involved in a shooting war with China, but it seems that Abe and other warhawks in Nagatacho want to, so the US should sit back and let them (once Japan's military is strong enough). I can't see the US getting dragged into a war that Japan starts - agreements with Japan are to
protect Japan against aggression, not actively assist Japan's own aggression.
This would be true, but I haven't heard of it. Maybe a source?
Like I wrote above, the US as actually been very supportive of Japanese rearmament. Here are a couple of articles:
Defense Secretary Chuck Hagel said in a statement Tuesday that he welcomes Japan’s new defense policy. It will enable their military to engage in a wider range of operations, making the U.S.-Japanese alliance more effective, he said.
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https://www.washingtonpost.com/news/checkpoint/wp/2014/07/01/japan-flexes-its-muscles-shifts-its-defense-policy-with-pentagon-support/
Here's an article from the Chosun Ilbo that references an article from the New York Times that suggests America is supporting rearmament:
http://english.chosun.com/site/data/html_dir/2013/10/07/2013100700985.html
Although the US is still saying it is committed to defending Japan, it does give Washington an option to restrain any defence, as well as allowing Japan the ability to ultimately develop a military to take on China whilst the US sits back and munches on popcorn whilst watching Japan do it instead of the US.
And back to Taiwan - no matter what alliances the US may have in other areas in the world, refusing to take on China in any invasion would not be a case of the US sending the wrong message to other allies. The US has no strategic reason, natural resource or other reason to protect Taiwan as long as it / Japan maintains control of Okinawa and the Ryukyu Islands. And like I wrote, if China is sitting in the former North Korea when it takes on Taiwan and the US risks unnecessarily losing 29,000 troops and potentially its relationship with Korea, there is no interest for the US to do so. Why risk having to take on China in Korea as well, with a limited force, instead of limiting the conflict to Taiwan and the Taiwan Strait? In such a situation, the US risks losing a lot more (and having the war escalate more rapidly) and I really think it makes no sense for them to get involved if that is the situation.