i always thought that prince ji, aside from genuinely being a jovial uncle with a taste for good music, also took one look at his brother's mindset and went to ruthlessly develop a bertie wooster image that would shield him from the emperor's paranoia most effectively.

This is also my impression. I also think he's a model for Yujin, or at least the Yujin we see in the beginning: very socially and politically astute, and mostly directing that astuteness at being uninvolved and seen as frivolous. (To be clear, I think this is conscious on Prince Ji's part and not entirely on Yujin's.) And as we see later with Yujin, Prince Ji is much sharper and more observant than he tends to let on.

I don't think it's accidental that Prince Ji survives much longer than the strategic geniuses.