The in-universe reason for her behavior is somehow way weirder than that, actually! This takes a bit of explaining, but I'll try my best to keep it concise.
So, originally, Princess Daphne was meant to be an homage/parody of traditional damsels in distress from classic sword and sorcery stories, in the same way the rest of the game is a parody of those elements (the lair is hyperlethal to a cartoonish degree, Dirk is a overconfident bumbling oaf that acts all stoic until he's actually in danger, most of the monster designs are meant to be evocative of classic Conan or Tarzan foes, etc.)
That's all pretty self evident, Daphne is a giggling ditz that doesn't do anything because the cultural idea of a sword and sorcery damsel in distress is that they're vapid arm candy that only exist to be trophies acquired at the end by dashing protagonists for doing something heroic.
However, when the time came to expand Dragon's Lair into a full franchise with its own TV show (done because the arcade industry was on the brink of collapse, and Don Bluth's video game division needed to scrounge up as much money from the IP as possible to keep itself going) they naturally realized that Daphne had to be an important character in it, and having her original characterization of "being the hot lady that Dirk saves at the end" from the games wouldn't really work for any form of extensive storytelling as a member of an action-comedy cartoon cast (even for a low budget tie-in one in the 80s.) So, they went for a different stock character archetype popular around that time: the put-upon clever female lead that has to wrangle in the stupid men in her life. Basically, the Dragon 's Lair cartoon is just the old Legend of Zelda cartoon, but with the serial numbers filed off and Ganon is a dragon instead of a pig.
Anyways, the show didn't do very well, only getting a single season of thirteen 30 minute episodes, but fans of the franchise DID like elements of it, and it's still treated as a canon prequel. Here's the problem, though: Daphne in the cartoon is a smart, no-nonsense adventurer who's often just as competent as Dirk. So... how does she go from that to the classic Princess Daphne characterization?
The answer is given to us by the Dragon's Lair comics that released to commemorate the series's 20th anniversary back in 2003, and it is...
The Author's Barely Disguised Fetish!
In the comic, Daphne starts out with her cartoon characterization as a spunky tomboy, even repelling an attack by Singe's minions by herself in a prologue story, but eventually does get captured. When she does, they finally explain what that weird-ass bubble prison actually is:
it fucking bimbofies you.
Literally, they describe it as it sapping your intelligence and making you more "frivolous", and make a point to state and show that Singe had used it on plenty of other princesses in the past, keeping them as his private slave harem in his treasure room.
Admittedly, it's a decently clever way to explain why a character would have two different characterizations between their major depictions, it does come off a little weird and tasteless? I'll leave that for the jury to decide, though.
I apologize for this not being as brief as I promised, but I think knowing why an initial characterization happened and then what the later justification for that characterization is was important to discussing it. But for anybody not wanting to sit through the whole blather...
Tl;Dr: Daphne is a weird ditz either because she's just another parody of sword and sorcery tropes OR she's basically a Mid-Bimbofication Princess Zelda, depending if you prefer your explanations Doyleist or Watsonian.
Use this knowledge as you wish, and thank you for reading!
