The problem with Lyse is the writing. She went from being a silly, but strong person who witnessed Alphinaud screw up with the Crystal Braves, has seen the monetarists try to frame her and her fellow scions for supposed regicide and yet is still somehow ignorant of how governments and politics work. She's also ignorant of how citizens work and thinks just declaring who she is should be enough for people to want to follow her.

The problem with Wuk is we have no real backstory at all, but we are somehow supposed to feel close to her or think she is the best leader. We see that many people don't support her at all in the beginning, but then suddenly at the end everyone is so happy she won?

Both are poorly written, but with DT it is partially the story itself (coupled with gameplay) that is the problem. The character is just a symptom of that problem since she's not the only poorly written character in DT. In Stormblood our time was split between Lyse and Hien. This is why I constantly say that if our character had been more "neutral" and split between the 3 contestants, DT would have probably been better. Constantly being faced with Lyse 2.0 is the problem since we don't have a Hien (Koana for example) to occasionally learn about.