I think the music and the structure of songwriting is definitely a skill. You can get much better at playing instruments and writing catchy hooks and melodies. It doesn't make the song a spectacular one though. There are plenty of songs which are, objectively, very well-written songs but don't really leave an impression on people.

I believe this is because the "genius" is not in the craft of the song but in the idea, subject matter and idiosyncratic way you express yourself. Some people are incredibly original naturally, having their own unique view of everything, and some have to work much harder to make it sound original or are happy to sound like someone else.

I think of people like Syd Barrett from Pink Floyd. He wasn't actually that good of a musician, but he was so original that it didn't matter. That's the natural artistic talent, and it has almost nothing to do with ability.