You may be reading a bit too much into it
Nope. But it's a general observation on Japanese vs Western culture. JP culture is fundamentally hierarchical. It's absolutely embedded in behavior and in language. It's fundamental in language. E.g. "Sempai" vs "Kohai". E.g. "Oneesan" vs "Imouto" (rather than just saying "sister").
This manga is just another example. The whole thing is fundamentally structured around a (humorous) struggle for supremacy (hence "battle" in every chapter title). (Though a big part of what makes the manga interesting is how much the top/bottom positions get flipped around.)
I like JP culture, but there are times when I just have to shake my head at it.