Is there actually a practical purpose in these exercises? Or is it a way to intimidate North Korea and remind them of the US's military powers? If not, couldn't they just hold these exercises somewhere not near the North Korean border?
Reminding North-Korea about the US military power is a reason.
Officially, North and South Korea are still in a state of war. There is an armistice, but despite that there are still regular incidents where it comes to weapons being fired by one side and/or the other. The relationship between the two countries keeps being hostile. There is a constant danger that this conflict might flare up again.
When North-Korea invaded South-Korea in 1950, South Korea was only able to repel the invasion because the United States came to their aid. The United States are still committed to protect the South-Korean independence. The regular joint military exercises between US and South-Korean military forces do not just serve as an exercise to improve the coordination between them in case the Korean war becomes hot again but also reaffirms to all powers in the area that the alliance between the USA and South-Korea is still stable.