I agree that the plot lost its way, and was further hamstrung by multiple jumps in time. But I was never bored, and not once did I think of dropping it. I became a fan of the Uncle Han Son character, and Song Sun Mi (who was similarly delightful in Start Up) does arch b*tchiness like no other.
It's hard to believe that the two leads could maintain their innocence and naivete after years of grifting and going undercover, but sure, why not? The main value of Private Lives for me was that it led me to the writer's masterpiece, Heartless City. Having binged on that, I can forgive the zigs and zags of Private Lives, which lacked the former's compelling leads and big budget cinematography. Netflix - I beg of you to do Heartless City Season 2!!