
The older sister is disabled, whereas the MC is able-bodied, but just doesn't want to train as hard with a sword as her brothers because she never thought she could win against them anyway. There's a difference between not being able to train to get stronger, and not wanting to train to get stronger.
It's also mentioned that the brothers don't see the older sister as a competition anyway, since she has a weak constitution, she will die during the succession battle anyway. They view her as more of an easy sacrifice when it comes to the competition.
Now that the MC has her smarts and self-esteem from her past life (had her degree in engineering, which is definitely not easy to get), she's more than capable of competing.

Well it showed that she trained a lot in the past, just nothing developed. Even then her brother looks at her now she’s “no color” in terms of her threat level. You can tell this threw her off because she had trained and recently started physically training again but it still doesn’t show.
What puzzles me is before they started to look favorably on her intellect and inventions they thought she had no power. Since the family only looked at physical strength and aura, which she had neither. So it seems weird that she wouldn’t have also been disqualified/exempt based on the family values.
By their standards the family sword wouldn’t have been able to absorb anything from her to strengthen itself.
Also the whole sword absorbing their abilities is weird too, is it their potential it absorbs and grow or the level of power they have when their absorbed by being killed by it? It makes it seem like when they die by it their power is absorbed, so killing a bunch of kids seems like a poor way to strengthen it. Also the past dukes seem to have died in battle, willingly/almost by suicide shouldn’t they kill themselves with the family sword before passing on the title since they want to strengthen it?
Also if they’ve done this for generations shouldn’t the sword be plenty strong enough already? Especially the current duke seems to only do it out of necessity/duty not because he wants to. Which also brings to question why is he ok with sacrificing his “pathetic” “powerless” youngest daughter? Now having her compete makes sense since she’s seemed strong.
Also it seems like their greatest enemy was that centipede in their domain, now that it’s gone you’d think they’d relax a little…
Also it’s weird that none of the other nobles seem to know that none of the successor candidates can leave the north until only one is left. Like it seemed only the northerners were aware of this.
Like it seems like part of the issue is involved with the royal family, but there just seems to be a lot of inconsistencies that just make it confusing… ┑( ̄▽ ̄)┍
I don’t understand why only the older sister is exempt form the succession battle? If it’s because of her health and lack of talent, wouldn’t the MC fall under the same category based on the family’s standards?