Look, book-Sophie's arc is dear and personal. Because she is an eldest sister, and so much of that is to her advantage in the story. She knows how to quell tantrums and knows how to run a shop and knows how to clean and make a home worth living in. The story would be infinitely sadder if Sophie was one of those "not like other girls" who couldn't cook or clean. Sophie knows that loneliness is the worst, leading her to talk to Calcifer enough that she knows how to break Howl's spell. Being bossy enough to get small children to stop fighting lets her deal with Howl and Calcifer's moods. Being unwilling to burden other people led her to talking to things, which is the essence of her magic! She acts like this because she's the oldest and knows how to take care of other people's hurts without them feeling like they have to take care of her. People can depend on her.
Sophie knows how to make a home from the start because she's the eldest and has been helping for ages. It's a great and wonderful thing that she knows all this!
What's terrible is when she think that it was all useless. She's cursed and her sisters are busy courting, her stepmom got married and sold the shop, no one in the town she grew up in recognizes her, the wizard she lives with can't stop whining about her cleaning to figure out she's bespelled and could really use some help, and she's right back at her father's shop a month after leaving.
But it wasn't useless! She and Howl just didn't have the communication skills to get her to know that. Her sisters are desperate with worry! They ask everyone, even Horrible Howl that eats young girl's hearts, for help in finding her! They have a reward posted for any information about her! Her step mother recognizes her almost on sight! Her sisters run to her the second they see her. They love her and their lives have been less without her. The skills she used to build up a home in the moving castle is one of the reasons Howl, Calcifer, and Michael love her and trust her with Howl's heart and Calcifer's life. Howl is actively returning the care she put into their home by consulting all his wizard friends about her curse to get to the bottom of it. (and is too busy to actually be courting anyone) Being nosy and bossy let Sophie see other worlds and get her the adventure she has never believed herself capable of.
That's what it actually means to be the eldest daughter.
Her manta "Of course I failed, I'm the eldest of three!" both pulls the reader to identify what is being constructed and deconstructed, the role of elder sisters and puts the reader in the odd position of thinking "what a self-aware fantasy character!" and "what a stupid thing to let stop you!"
One of Sophia's main internal struggles is about a fear of failure because the world tells her she's going to fail. Then she fails and immediately goes to the conclusion "the world was right, I am a failure for this arbitrary, uncontrollable trait."
Sophia escapes this mantra for the first time when she's old and is like "well, who cares what they have to say now. I'm old and earned the right to do as I please". The thoughts come back through, the way messages telling of hardship and failure always do, but she doesn't let it stop her anymore, not like it did the first months of the book. Why?
Because what being the eldest daughter actually means is cleaning up messes because no one else is going to clean yours and your siblings are too young to clean up theirs.
Sophie is pulled into plot points almost exclusively by the need to clean up her mess or help someone else. Gotta protect Lettie from Howl catching her heart and breaking it! Gotta help Michael with the spell! Gotta free Calcifer who can't break his own curse! Gotta help the poor dogman that hates Howl! Gotta help Miss Angorian, even though she's a beautiful lying manstealer! Gotta kick Howl out of his despressive spirals! Also gotta help Howl by blackening his name before the King (no one said helping couldn't be fun).
Ironically, the very trait the world told her would make her unsuccessful was crucial to her success. She's scared to fail like everyone has said she would, but she doesn't stop trying to help people anyway, in her eldest daughter way, and she succeeds in the end and rewrites fate. I love her.