I find it odd that the demons who seem to value strength over all else are so dead set on going to war for a princess that was weak enough to be captured by humans. You'd think with their mentality it would be a good riddance to a weakling type attitude. Although, that schemer may have had a hand in getting the princess captured in the first place to set the stage for war and while the strong fight and die, he'll usurp authority.
It wasn't really that she's weak. The manga just skipped
how she was captured, but the novel covers it. It also sets the background as to why an ossan is able to go after someone so young.
In the novel, it's explained that she was captured because while she was having fun traversing incognito in her human transformation, she was drinking at a pub with some strangers and as she got so drunk that she passed out then the transformation was undone and so everyone saw that she's a demon and so she was captured while unconscious and then woke up in a cell with those magic-sealing cuffs on her.
She explained this while in Cain's mansion one of the times they talked before they headed to Seto's country, so this is not a spoiler; the manga simply skipped it.
So essentially, she's old enough to drink alcohol, and she was never captured by being overpowered. So she's not weak, she just got too drunk.
Except might doesn't make right 100%;
Does the story ever mention why she's beloved by the demon people despite not being strongest?
Think of it more like in Japan, where the leader of the country is the prime minister but they also have a royal family. That's why the royal family's status is so high in this story, as their lineage goes back to the founding of the empire.
Plus, the story explains it in the novel that the beauty of Lisabeth is something that has made her the sweetheart of the empire, and admired by the people. It's also part of why Dennis got those pervy eyes set on her.