Enchanted fishing rods to carrot on a stick?

I feel that if your fishing rod is enchanted you shouldn’t be able to craft it into a carrot on a stick. (Story time: I’ve been fishing for a while with my lure 3, unbreaking 3, and mending rod, when I finally fished up a luck of the sea 3 rod. I combined them and continue fishing with glee, after that I went to go make a shovel and I misclicked and made my super op enchanted rod into a carrot on a stick.[ carrots in my inventory ] I strong hate the fact that I have to build up to obtain this op rod again and that I have to rely on a plain rod to get it)