"... Koreans ... stay long enough to give birth so that the child will be American and can avoid compulsory ROK military service later on."
They may be in for a big surprise "later on." Here is what the U.S. embassy in Seoul says about this:
"South Korean men over the age of 18, including American citizens of Korean descent, are subject to compulsory military service. ... There have been several instances in which young American men of Korean descent, who were born and lived in the United States all of their lives, arrived in the ROK on a tourist visa only to find themselves drafted into the South Korean army."
Warms my heart to hear that.