The older brother didn't abbandone the FL because he wanted but because the step mother send him to study, he didn't have a choice since he couldn't become the Duke because he was too young when his father died. Also the step mother literally closed every type of contact between him and the FL. Also even if his friend is the 1st prince of the country, he isn't the crown prince yet so he doesn't have that much power at the moment,but even if he was capable he was going to get in trouble because the step mother was the temporary head of the house and also because they didn't have proof of the abuse since the FL never showed out of the house until the start of the story and there were rumors about her having a mental illness.
Let the younger brother, Rudolph, succeed the duchy. At least he's sweet and may grow up to be a decent person. The older brother is a shit stain who abandoned his younger sister in an abusive home and made absolutely no attempt to help her. His best friend is the first prince of the nation, and yet somehow he didn't think to send someone to protect, or at least check on her over the years? He couldn't say to his best friend "hey, you're the prince and my sister is being abused, can you do something?"
But nope, he just abandons her. He can just stay away and keep adventuring with his friends. MC doesn't need him.