I don't think Leela's character is a "sacred cow" at all. Most of the episodes which center on her also center on her flaws, of which there are many. Off the top of my head :
- She has poor depth perception.
- She wears size 12 shoes (Rebirth) and other characters have twice complained that her feet smell when she takes them off. (Anthology of Interest I, The Farnsworth Parabox.)
- She is the worst blurnsball player in history. (A Leela of Her Own.)
- She can be a raging hypocrite. (31st Century Fox, ITWGY, The Mutants Are Revolting.)
- She has terrible taste in men. (Alcazar, Sean, Adlai, Chaz, ZAPP BRANNIGAN.)
- She can be obsessive. (Mobius Dick, Bender's Game, Anthology of Interest I.)
- And petty. ("I wanted the end locker. It's not like Amy cares, but oh no, she won't trade with me . . .")
- Also interfering. ("Fry made his own choice, but he made it wrong, so it's now it's time for us to interfere in his life." - I Dated A Robot.)
- Not to mention violent. (Bender's Game has a whole plot strand revolve around this, but it features in most episodes.)
- But in her relationships with her parents and various love interests, she is shown to be emotionally insecure. (For her parents, see Less Than Hero and Teenage Mutant Leela's Hurdles. The crap she puts up with from Adlai and Alcazar is surely enough evidence of romantic insecurity - which she also shows with Fry on occasion. She's very insecure about her appearance in The Prisoner of Benda, and has a tendency to respond to Fry's romantic gestures rather than make them herself.)
- She's jealous. This may be simply reactionary, but she's frequently catty about Amy.
- For all the nice things she has done for Fry, she has also treated him badly at times. She was insensitive in The Why of Fry, resisted his attempts to help her in The Cyber House Rules, and blamed him for their brief marriage in TKOS.
- She is very quick to judge others. (Zapp Dingbat, I Dated A Robot, pretty much everything Bender has ever done.)
- She is stubborn, which often leads her to rash decisions. (Flying through the Bermuda Triangle in Mobius Dick, telling Fry to jump in the toxic lake in The Mutants Are Revolting, etc.)
As you can see, it's quite a list - and I like
She's definitely flawed, and the show has never shied away from that. Fry sees her as perfect, but the show doesn't always present us with the same Leela he sees. In TDHAIP, for example, Fry looks longingly at Leela . . . as she eats a huge, messy spider leg. In The Farnsworth Parabox he asks her repeatedly for a date. She fobs him off with the excuse of "sweaty boot rash", at which Amy chimes in with "No spluh! Why do you think I'm over here in the stink-free zone?"