its mostly because of the colour scheme of his kingdom! i know that royalty is typically associated with deeper, richer colours but his country's colours are white, baby blue and baby pink, and these colours (particularly blue and pink) are mostly reserved for the royal family;;; white is a bit more ambiguous since its such a common colour but in that case the difference is all in the materials and embelishments.. like if you put edenyj and eden bg side to side both in their casual day to day clothes and they were both in white you would still be able to easily identify who was the prince from the fabric alone

but as for why he wears mostly white! it /is/ bc of it being a signifying colour of the royals but its also the most plain of the three, since he wears his heart through his clothes its like his own personal colour scheme becomes more drab the more upset and hopeless he becomes, like he's losing his own colour as time goes on, but before wonyoung was cursed he had quite a warm colour palette, with lots of baby pinks and peaches and creams!