Again the newspaper Club closing down is only a problem for the school. It has nothing to do with the main characters. Just let it close down and let the school sort out its own mess. This entire Arc just pisses me off.
As the MC himself pointed out a few chapters ago, the problem is that if the club gets dissolved- or more specifically, demoted to a hobby group- that is not going to stop the members. If anything it'll incense and motivate them. So they would have kept sniffing around for scoops and scandals, and would have sooner or later found out about the trio's relationship. Which, as has been frequently established,
would be very very bad for them.
So yes, they are helping the Newspaper Club. But that's not their priority. Rather, it's
how they're helping the club; by showing them how they can succeed as a proper, informative school newspaper producing actual constructive articles relevant to the school and its populace. By doing that, the club members learn that they
don't have to act like paparazzi to keep their club afloat. Which means they'll focus their attentions and efforts on doing things the right (read: non-invasive and unlikely to expose the trio) way instead instead of sniffing around chasing rumors and gossip.
Additionally, helping the club puts the trio in their good graces. Since they owe the continued survival of their club to the MCs, the members will have all the more reason to
not print anything the trio doesn't want made public. What's more, there's also benefit for
Hikari too, who has very little she's personally invested in when it comes to school. If she ends up actually
liking being part of the Newspaper Club, she has all the more reason to maintain her regular attendance. More importantly; she'll have something that's all her own, not tied to or shared with Chikage. Which will do a lot of good for her development and help her have a more fulfilling school life.