I don't know what it is that makes this show as enjoyable as it is, but there's just something about it.
The premise is interesting but poorly executed, the writing is solid but the plot doesn't exactly make sense, the acting is great but the characters are underdeveloped. So why in the hell does it work so well then?
I can't answer that question with any certainty but I can sure try.

My favourite part of the show are the characters. Yes, they are somewhat underdeveloped and don't really have character arcs as such, but they are all incredibly, bizzarely charming.
Our prince is as sweet as sugar, he is a ridiculously kind and gentle person who is very inconveniently stuck in the body of a royal. He is almost as much of a fish out of water as Eun Ho and watching him doing his best is as funny as it is sweet.
Our bodyguard is the epitome of the tortured, brooding servant utterly devoted to his master and absolutely no-one takes him seriously. He waves around his sword and makes threats and vows to protect the prince with his life and mostly all he gets in response is "yeah yeah we got it, calm down and come join our cuddle pile instead".
Our hapless time traveller steals the show by virtue of being utterly, hilariously unflappable. No matter what happens to him, no matter how strange his environment is, he faces it all with an attitude of "Yeahh this might as well happen" and then simply gets on with his day.
The dynamic between the three is incredibly entertaining to watch and there are many fairly unsubtle hints at a potential polyamorous relationship between them, which makes the whole thing even more enjoyable.

So take all that, mix it with an absolutely gorgeous wardrobe and a story utterly devoid of angst, shake it vigorously, and what you get is this odd, off-beat, wholly charming show. It's not a good show by any common metric, but it is undeniable fun to watch and at the end of the day that's what's important.
So give it a shot, you'll very likely be entertained.