I hope Prince Wu hitting on Asami is actually a plot device that continues throughout the season in order to faciliate more Korrasami action during Book 4

aka Korra is constantly like “HEY CUT THAT SHIT OUT” or is glaring daggers at him or holding him dangling by his collar outside a high-speed train, etc. while Asami is all like “Korra, we are TECHNICALLY supposed to be his body guards, bring Wu back into the train.”