It's also hard to build that experience, that innate sense of storytelling, any other way. Part of learning how to tell stories is engaging with stories themselves.
I wouldn't go so far to say you can't be a writer without reading, but I do think you miss a lot if you don't.
And if, for various reasons, reading books aren't your thing there are SO MANY other ways to engage with stories. It's really awesome!
There are audiobooks and TV shows and movies and YouTube channels and D&D actual-plays. There are endless ways to tell and hear stories.