
Well I get your point but you need to consider that you can't just train and bam your much stronger. Her body was born in weak condition. There are limits bodys can achieve and hers is weak and gets sick easily so even if she would train her condition probably wouldn't improve much (Training takes many months/years too) And added it would be really weird for a noble woman to just start training, her body isn't a knight. She's woman who only had like nobel lessons and probably never even wielded a sword. She can't get support either because there are already rumors she's insane and well nobody would believe her she reincarnated. Additional she's not really popular so her only chance is to take advantage of someone who is in an higher position than her. Well and she's really sick and depressed right now.

Even if her body is weak it doesn't mean she can't get at least a little exercise. And I don't mean that she should swing a sword right away, but she said that even walking is difficult for her. Even a person with a weaker body shouldn't have a problem with such basic things, it's not like she's disabled or anything. Besides, even if there are rumors about her, it doesn't mean that through contact with other people she can't reduce it. It's my point od view tho (〜 ̄△ ̄)〜

she just got killed by her best friend, found the kingdom she worshipped the groun of was destroyed three years ago, had to get engaged with the enemy, ended up with a situation and body the opposite of her own, is just going past her internalized misogyny (as she said when she stated herself that she didn't like the other noble ladies back then but now respects them), and found out that the same best friend is dead and that her subordinates are somewhere out there and unsafe. she's very, very desperate right now and let's say she /does/ exercise and somehow, despite her canonically weak body since day 1, it works, what is she going to do? get swordsmanship training? she just asked about why ladies have to talk a certain way and stress about etiquette when noble men don't need to and she got shot down immediately.
right now, she doesn't have any attachment to the ml and her only focus is getting revenge against khalid and her empire. of course she's going to see the advantage she can get if she uses the ml. she's a knight of her country first and the commander of said country before she's a noble lady. she's just choosing the best option.
I hate second ML and also FL. She knows she's weak, but instead of training and securing other people's support, the first thing she thinks about is how to take advantage of first ML ヽ(`Д´)ノ