I think it's just a matter of preference.
Others, as weird as it may sound, want their partners to be possessive of them. And think that if their partner isn't like that, it would somehow mean that they don't care about them. So it may be linked insecurity. Or perhaps for others they just want their partner like that or smth.
In real life, it is indeed suffocating as hell... but i just love seeing it in some Mangas. for those that don't really have a well built up plot, it does make the story move smoothly, but if there were a great plot and built up relationship, then it's going to come out so weird. For this story, they needed the possessiveness cause it was so rushed. even tho, this level of it was just meh.
Bearable, I guess... I just don't know why possessiveness is so normalized in most stories, that most ppl think it's romantic. I personally find it suffocating.