Rhee was a political animal for a long time - from 1897 when he was jailed for demonstrating against the Yi, right down to a far more recent time. Certainly he was influential if we can talk about what he was up to more than a centurylater.
You have to evaluate Rhee in terms of the factions ruling China (since his "government in exile" was set up in Shanghai - at some point he was removed from that organization as China fell under the Kou Min Tang, originally an affiliate of the Soviet Union). You must also evaluate Rhee in terms of what was going on in Japan since the ruling Meiji faction held power until the 1930s when the militarists with their Nazi connections took over.
The fact that Rhee seems to have little contact with the militarists in the 1930s doesn't get him off the hook when it comes to Meiji factions that had ruled earlier, and it is to them that I am pointing. In fact, they are the folks who took over Korea, and not everyone opposed them. Their destruction of the titled nobility was probably viewed very positively by the peasantry as well as by the educated intelligentsia.
After 1945 Rhee brought into positions of power men who had been cooperative with the pre-militarist Japanese colonial government. (This gives us two different Japanese puppet governments - one which actually had some ambitions to improve the whole region, and a later one which had as its purpose organizing Korea to support Japanese war needs.)
Standard histories written in the US or by Rhee admirers tend to protect Rhee, Roosevelt and the Progressives.
Joseph Sutton (now deceased and formerly President of Indiana University, and earlier an OSS senior analyst) frequently brought up Rhee in his lectures on American Pacific relationships. He was never complimentary. He didn't like Teddy Roosevelt all that much either.