USA also does not stamp passports anymore.

Also, signing up for one of the trusted travel programs may help in some countries. I don't even need my passport anymore in some countries - just my ugly face : )

I have Japanese and Korean friends who have US citizenship - and have not renounced their citizenships. They just enter and exit the USA with their US passport and enter Japan and Korea with their Japanese or Korean passport. My Japanese friend says Japan knows he has a US passport but just doesn't care. I think it is the same for Korea.