Author-sama doesn't need to make Moe-chan into a bitch to decrease her popularity. We already know she is an unserious losing girl and far behind the other two.
I don't think the way Moe is acting here is anything new, she's always been headstrong, her calling Hebikawa out doesn't make her a bitch.
The thing about the war, as you put it, is that the Snek-haters pretty show up to trash on Hebikawa, on grounds that she offend their sensibilities. As evidence, I present to you idiot #1:
This guy is owning "the libs", except "the libs" here is a fictional girl who's also nothing more than bully. It's silly, it's like they're self-inserting themselves into every pore of the story. I've also never seen this guy nor idiot #2 having anything to say about Kusunoki beyond "um, she's a good person" either.
The development is a good thing, but for some of us, it's just lost love at this point. Also rather than pointing out that Kusunoki is more reserved than Hebikawa, it's better to just blame the author for not giving us Kusunoki's backstory sooner. If the author had done that, there would've been more chances for bonding scenes between her and Keisuke and there would also be more Kusunoki fans in here too. This really is just a lack of experience on the author's part.
I'm not sure if posting like this is necessary nor do I know who this "idiot #2" is you're referring to but as far as Kusunoki goes, her being kind and sweet isn't a bad thing.
I'm also enjoying how conflicted she is about the whole situation, as far as her backstory goes, yes, maybe we should have gotten some details sooner but I'm still happy with how things are developing.
I was wondering why even make Moe part of the love competition when it barely impacted the dynamics and she clearly has no chance (plus there was already a love triangle of sorts at play), but I guess it was about the "2 girls falling for the same guy and still being friends" bit that Hebi talked about this chapter. So if they keep their friendship strong even after this is over it would prove Hebi wrong so this is probably where the author wants to take this.
Moe is sadly the designated loser girl and her role like you said is to help prove Hebikawa's beliefs wrong, which ultimately is a good thing since Hebikawa does need to change her ways and have a more open and less twisted view on life.