I think it's undeniable that every member of TWICE loves each other. Even though there are nine personalities among them, all have such a close bond. That said, there are pairings that work better with some over the others. Chaeyoung, for whatever reason, somehow mixes well with all of them. It's like she's the protagonist in a harem anime. They all have a soft spot for her but in different ways. Jeongyeon likes teasing her. Jihyo likes protecting her. Sana, Momo, and Nayeon like playing around with her. Dahyun is her bro. But Tzuyu and Mina are hardcore soft on her. They both find her too cute to handle, and often break their usual quiet and elegant personalities when it comes to Chae. Mina is more subtle and shy, while Tzuyu is pretty bold when it comes to her affections. I think that's why there is a shipping "war" between Michaeng and Chaeyu. Both Mina and Tzuyu are so different when they are around Chaeyoung that it's cuteness overload. Meanwhile Chae, like a harem protagonist, plays innocent to avoid being caught in the middle.
I've always thought the same! Like obviously all 9 are close and love each other, but even some members admit that sometimes left alone with each other, it can get awkward like we have seen with recent twice dates between Natzu and Mohyo. But Chaeyoung? She truly just seems like the center of twice in that she has such a unique relationship with each of the members. But like you said, the shipping 'war' between Michaeng and Chaeyu probably is due to how soft Mitzu are with Chaeng.
I want to see a TV show with Mina, Tzuyu (the parents) and Chaeyoung (their bratty daughter). It could be a comedy with dramatic moments occasionally. Get on it JYP!