I like Dowun not because he's a good person or anything but just because he provides the story with forward impetus and emotional weight. Whether you like Dowun or not, moments like the princess selling her earring for some steambuns wouldn't mean anything if Dowun wasn't the character that he is. Baek is kind of flat as a character, with little in the way of depth and being a rather one-dimensional moral agent, but also by existing and providing Lyon that alternative to Dowun helps to make the outcome of the story uncertain. If it was just one or the other then this story wouldn't be worth reading.
There's a reason that this formula of having competing male leads is so common. It's a mechanism for providing tension and keeping readers invested and engaged, arguing with each other or internally supporting one option over the other. For comparison, look at, say, The Duchess with an Empty Soul. That story has only one route/ML and is completely uninteresting. I would much rather read a story with both Dowun and Baek than one without either.