Poly isn't my personal bag, and I think despite how some poly people think it will never really be workable for that big a minority of people. But I'm happy enough to see it work for the people it works for, whether in reality or fiction. I don't like ratatouille either, but you don't see me hating on that movie about the rat and French cuisine just because he wins the critic's heart with ratatouille.
I've only seen one three-girl poly relationship in manga before, I believe in Ano ko ni Kiss by the same mangaka where it was just one strand among many. This was done better. The other one it was just, the one girl liked two other girls and the other two kind of ended up dealing because that was they only way they could have her--there was no real development from rivalry and even dislike to OK threesome. In this you could see the girls' growing respect and attraction for the "other" they weren't initially in love with. It definitely feels much more like it can work and they could all be happy together. In the end, I buy it, and it's pretty sweet too.
(I find them blithely telling everyone they're in a lesbian threesome and this being apparently accepted somewhat less believable, but I'm willing to go with it in the tradition of the "Morishima Akiko" style nobody-is-prejudiced alternate yuri universe)