I can't see a use-case for Functional Programming. It seems a step backwards

It's just like procedural or object-oriented programming: an approach to solve problems. There is no specific use-case, it's just another way to look at things

I think in theory, you can't get more elegant. In practice, I find it hard to read. The functional programs I have written have been fairly bug free, but when I compose a bunch of functions together to accomplish some business rule, I have to pick it apart every time I read it because it's so hard to follow.

I think it's great for coding challenges though.

It's good for things like simulations and scientific programming where the reader knows what the author is expressing mathematically more easily than conceptually/an inheritance structure.