Strategic & security interests. The United States need to have its fleet and army personnel stationed in Japan and South Korea to maintain a power balance in the area.
The Pacific Ocean is fairly "empty". Going east from the Japan Archipelago, there are few places where the US could station military personnel until one gets to Hawaii, around 4000 miles or 6000 km to the east of Japan.
Let's imagine a case where American soldiers leave South Korea and North Korea invades. Had there been no military bases to the west of Hawaii, it would take a long time to send military personnel to support South Korea.
Moreover, Japan officially doesn't have a military, and its defense expenditures and equipment are very limited compared to other countries of such size. Neither does it have a military draft, not even in times of war. South Korea does have an army, but North Korea's army is just much bigger. There is no way that South Korea could possibly have an army comparable to North Korea's. In the event of American evacuation from East Asia, a North Korea invasion (or at least aggression) would certainly be the case.
There is little possibility of overt military aggression by China, but there is still a concern here. If the US does not maintain military personnel in East Asia, it could eventually lose its grip over South Korea and Japan due to China's proximity to them, large trade volume with them (a FTA was almost signed), and of course China's ability to use force deterrence. South Korea and Japan probably wouldn't choose communism (or even less possibly Chinese style "socialism"), but they might turn to China as their main partner! So, to keep its grip over South Korea and Japan, the US has no choice but to continue to provide security to the two countries - by stationing troops there.
Do Japanese and Koreans like the G.I.s in their countries? Probably not too much. There have been protests against American military presence in both Okinawa, Japan and South Korea. However, do they want American soldiers to leave? Neither, because there will be unfathomable consequences to this.