@comeonnow The situations are different in material, obviously, but the same principles apply with regard to the legitimacy of his new friend group getting involved.
On the other point, it's a drama/comedy manga first and foremost. The plot is driven by drama, and most of the chapters will be centered around drama, spiced up by comedic elements. I wouldn't recommend continuing to read this manga if you don't like that, because it will likely be continuous drama going forward.
Not saying that's not a valid critique, just that it's likely not going to change.
Additionally, it does make sense. Anyone that only studies for exams and does not take the time to balance themselves out with hobbies or interests is just going to burn out. They've also said he already spends the time at home practicing kendo anyway, and the situation still clearly weighs on his mind and affects his mental state when he's reminded of it. Assuming they're still studying properly, it's only a net gain to the study group to get this issue resolved, especially since Nagi is a spaz and can't focus on anything else.