The task indeed falls to parents to inculcate a reading habit in their children. They should deliberately make their children read. It's through reading we acquire pieces of knowledge that can change and refine our lives. So any parent that's not teaching their kids to read is raising them wrong. The screens has done more harm than good to our society.
If parents aren't interested in reading themselves, they are unlikely to support their kids in it - other than telling them to read more. I tis like parents telling kids to eat healthy and exercise, when they themselves don't do those things.