I don't understand why 'should writers read?' is even a question. Do we discuss if musicians should listen to music? If chefs should eat other people's dishes? If carpenters should sit on a chair made by someone else?!
If you're strictly doing things for yourself, sure you don't need to consume other people's works to learn. But if you want to make it into a profession, or at least become good at it, there are standards to be met.
I think this discussion comes because we all already know how to speak a language and use it. So writing for some people might not look that different. And that's wrong because writing is a different craft and it's an entirely different skill.
