I get the feeling the teacher is playing some 4D chess here. Hikari's been slacking off of school so much that her attendance is shit, to the point that Sakuto had no idea she existed until their first meeting. Chikage is a diligent student who wants to do her best but IIRC both struggles under pressure and dealing with other people. Meanwhile Sakuto has been doing his damnedest to be as unremarkable and "average" as possible and actively hiding his capabilities.
=Hikari being motivated to take part as a member of the school newspaper gives her something to be passionate about and a reason to come to school that's all her own.
=Chikage being the one having to handle this particular audit gives her valuable interpersonal experience, particularly when it comes to navigating between making people happy and doing her job.
=Sakuto is forced to actively apply himself and show what he's capable of in helping the twins navigate this sticky situation, breaking him out of his "don't be the nail that gets hammered down" mindset.
All while the teacher gets to take a hands-off approach to dealing with the messy audit business.
This is it, yeah. Sensei is definitely presenting as a lazy manipulative educator, but her scheme here actually
does benefit all three of our Main Throuple, while also making her own job easier by not dealing with the (presumed) headache that is adjudicating club stuff.
Plus, we've been shown that the teacher has some sort of vested interest in Sakuto before now; I'd have to go back and reread as to whether the
reasoning has been revealed or hinted at in some manner, but this isn't the first time she's directly meddled in his life, and by extension the twins', in order to affect some change that sees Sakuto coming out of his shell a bit.
So Sensei's helping herself, and it probably does carry some pragmatic reasoning like "I really just can't be bothered", but this plan of hers covers all the "pros" you mentioned, and also further cements the notion that she's got some bigger aim in mind where it pertains to Sakuto, especially.
After all - she's giving
him the actual information and push, each time (same as the inter-school festival committee arc). Chikage is smart, but Sakuto's the one being compelled to actually "show up" and stop hiding himself away.