I can't think of any anime scene in general where the power of friendship bent the story conveniently.
I've seen that many people name Fairy Tail as the number one anime guilty of power of friendship but I don't really know what they mean. I mean it seems logical that working as a team makes one stronger. And of course it boosts morale if you have someone to protect or if someone is there for you.
Since Fairy Tail is a battle shounen you will see the protagonists defeat one strong enemy after another but that's just what a battle shounen is. In the end it comes down to whether you can enjoy it. If you can enjoy it when the protagonist keeps reviving after being defeated without any reason then it doesn't really matter. And in Fairy Tail I don't remember seeing anything that destroyed my immersion but it might be different for you. And judging from what I've heard from you before you probably won't like Fairy Tail but you never know until you try. If you just watch until it's no fun anymore than you at least had fun for some episodes.
And now that I thought of it I remember being very shocked when Wendy did cut her hair during a fight resulting in me looking up whether it would stay this way but that's just because I liked her long hair. And yes, her hair returned to normal after this arc.