I suspect US Military presence is not necessarily for the purpose of spreading Democracy.
Commerce, however, does provide a great opportunity for “building bridges”. This works providing fundamental values are not at stake. My SK contacts are Christian.
The US military is still needed in South Korea, not to spread democracy but to protect it — and to prevent an Asian nuclear arms race.
South Korea’s strategic situation is dominated by China’s looming presence. Korean history has many episodes of Chinese or Japanese domination, with Koreans prone to describe their situitation as being that of a shrimp caught between whales.
From the South Korean perspective, the dangerous and crazy North Korean Chinese client state requires that a powerful and mostly acceptable foreigner (the US) be a counterbalance to Chinese influence and a guarantor of Japanese good conduct. But national pride urges South Koreans toward being able to stand on their own.
The soft aspects of troop quality, training, doctrine, and experience matter greatly and are often harder to get right than military technology and weapons. From what I have read from experts, the South Korean military is not yet up to the demands of modern communications, command, and control and a long planned handover of headquarters functions was delayed.
On the other hand, it would be relatively quick and easy for South Korea to make nuclear weapons and a missile delivery system aimed against North Korea and implicitly against China. Nuclear weapons play to the strengths of a modern industrial society in producing expensive, technology driven products.
A South Korean nuclear capability would do much to keep North Korea and China at bay as US economic and military power decline. As long as the US military is needed in South Korea though, we have a veto against a South Korean nuclear program. That means that Japan and the Republic of China do not have a clear justification for going nuclear, with follow on effects as other countries did the same in response.
In a roundabout way then, the US military presence in South Korea benefits China as well as South Korea and helps keep the world from having a dozen or so new nuclear powers.