It's more of a quid pro quo, and Asian communities strongly value familial piety. She is also emotionally broken down. So, when you put these three facts together, she doesn't want to be cast out by her family because she doesn't know how to function without money.
Imagine going from high 6 figures your whole life, then BAM, you're on your ass. People have killed themselves when they reached that point.
She wants the company her father has, but he won't give it to her; if he did, it would be, "Do this for me first, and I'll give you the company," but that becomes a slippery slope fast.
So usually this trope is deployed when they want a character who very much can't live a normal person's life and needs to stay in the family.
Yeah, I get the whole cultural reasons. But it generally always rubbed me off the wrong way this trope in particular.
I felt it specially bad in this yuri manga called Citrus.
The love interest, Mei, who was part of a rich family, her granfather the school headmaster, wanted to have her marry a guy. And adult, who was her teacher on top of that. And the guy was even sexually harassing her while I think she was still a minor, while also sleeping with a different woman, because he only wanted this girl for her money and family influence, no interest on her as a person whatsoever. Mei knew all of this, I think, but never told her grandpa because she thought she couldnt just say no or opose this guy.
But then FMC reveals the truth and the whole thing gets broken when the grandpa realizes the fiance is an asshole.
...Then later Mei abandons FMC for reasons, which includes her grandfather telling her AGAIN to marry if she wants to inherit the school, which she wants... for reasons. Because theres this whole weird subplot, where the original inheritor should have been her father, but he pretty much became a happi and gave up on that duty (and his daughter as well, from what i remember) to live the life he wanted. So Mei ends up being raised by her grandpa, forcing herself to abandon FMC because she thinks its her duty now and cant escape it... In the end it turns out the grandfather, tough and all, could simply be convinced if they talked with him. As some years in the future she owns the school and its on a public relationship with FMC.