I really like to read comments about this manga. There is a lot of good insights, it's pretty interesting.
As far as it goes for me, the main point of the story isn't Yuri. Sure, the genre of the story is Yuri and it's an important part of the story. But for me, as it is in YagaKimi (since you are all making a comparison), the most important thing is that characters have to free themselves from other's expectations. It could be from relatives, society, co-workers, friends, parents or even themselves... The fact that in both YagaKimi and Crescent Moon, it is (partially) done thanks to their partner is kind of irrelevant. Sure if it wasn't Yuri, I wouldn't be reading those, but the main point in those stories is for characters to grow and embrace who they are.
This is why there is scene like the one with Sakagami. In those stories people change both themselves, how they see other people but also others as they evolve. I wouldn't be surprised if Hinako ends up having a positive influence on her coworkers. This is why we can relate to them so much and why it's so interesting. The fact that it's yuri is secondary I think (even though it's my primary reason for reading it :p).