Is there any reason why the Americans in general can’t just put Rhee in his place?
Other than the fact that ignoring or threatening the Man, who is the President in the Nation that they are trying to protect, is a really bad idea?
One should remember that Rhee had a lot of powerful friends in the United States. Before his authoritarian rule over the Republic of Korea, Rhee spent a lot of time in the United States and in the Korean independence movement. He had converted to Christianity in Korea due to his involvement with the American Missionaries in Korea and this open a lot of powerful connections for him when he came to the United States. He actually became friends with President Woodrow Wilson and his family and attended worship service with them.
When Korea was eventually liberated, Rhee got a lot of influence and political cred as he was one of the very few Korean independence activists, who refused to give up on the cause of Korean independence. By the 1930s, the majority of Korean independent activists believed that Korea would forever remain in the Japanese Empire. Not Rhee. Throughout the 1930s, he kept pressuring the US State Department to aid Korean independence to the annoyance of Secretary Hull. When Korea was liberated, he managed to become President of Korea partly not only due to American support but also due to the fact that he was one of the very few credible leaders who was not tainted by past collaboration with the Japanese. During the years of Japanese occupation, most Koreans did collaborate with the Japanese to some extent. Rhee was one of the very few who didn't because he had to flee Korea at a young age and worked in the Korean independence movement aboard.
In addition, Rhee's distrust of the United States is not unjustified. Rhee's resentment and distrust of the United States can be traced as the result of a meeting he had with Theodore Roosevelt. At the time, Japan was about to completely annex Korea, the young Rhee, and the Korean delegation he was traveling with desperately needed American backing to prevent the Japanese annexation. President Roosevelt met with them and told him that he would consider it. Rhee celebrated this until years later when he realized that TR was playing him and had no intention of giving American support to Korea. TR had merely indulged him in order to prevent Rhee and the Korean delegation from messing with his own plans regarding Japan. Rhee remembered this and never forgot the lesson. That despite America's commitment to Democracy and Freedom, America was fully capable of abandoning causes that they dislike or have no interest in.
During the Korean War, Rhee was in a very difficult situation as he could not afford to let South Korea be seen as the United States lapdog, while at the same time he needed to maintain American support. This meant, he often felt that he had to be difficult and uncooperative with the Americans in order to assert South Korea's national sovereignty as Korea was occupied by US troops and there were plenty of accusations that Korea was being turned into a colony of the Americans. Obviously, the Americans were constantly pissed and angry at Rhee because he kept getting in their way and was very uncooperative. At the same time, the Americans could not move against Rhee because, at the time, the South Korean people overwhelmingly supported him because he was seen as defending the Republic of Korea's national sovereignty and the Korean people like Rhee wanted to reunify the Korean Nation.
One of the biggest examples of the Americans considering putting Rhee in his place happened during the Armistice talks. The South Korean people overwhelmingly opposed the talks as this meant that Korea would be forever divided. Rhee, who was aware of this, unilaterally released thousands of North Korean POWs in protest of the United States' promise to repatriate NK and Chinese POWs back to their nation regardless of whether they wanted to return. The United States was enraged by this and seriously considered overthrowing him, but they realized that they couldn't because the South Korean people overwhelmingly praised Rhee for his actions. Thousands of Korean students went to the Blue House and celebrated Rhee for his stern opposition to the Armistice talks, thus the Americans could not overthrow Rhee without losing their credibility with the South Korean people.
Obviously, the Rhee administration was extremely corrupt and seriously violated the civil rights of the Korean people. He was an authoritarian leader who kept power through undemocratic means and suppressed the civil liberties of the Korean people. At the same time, he was competent enough to defend and advocate the Republic of Korea's foreign interests, which was vital for South Korea's survival especially during and after the Korean war.