Rhymes? Some good songs dispense with this mostly or entirely. Often enough people don't notice. (Deportees, for example).

I don't think there are any rules for how to write songs, none that you can't find exceptions to, anyway. What there are instead are people's experience of the way they do it - and even there I'm pretty sure it's only some of the time they actually do it the same way.

Story - there are plenty of songs where there's no story, or where the hints of a story would be filled in by different listeners in a completely different way, and that's where the song gets its strength.

What do you need for songwriting is a bit like "what do you need for cooking".

Mind you, that wasn't a complaint about the thread topic, it's coming up with some very interesting responses.