First of all, I suspect that people with ADHD are attracted to screens, and they don't necessarily CAUSE ADHD. For DD in particular, they seem to calm her down.
That being said, my kids would be on games like Minecraft all day if I didn't limit it, so I started making them EARN screen time. Otherwise, they don't get any. Right now DS is reading a chapter book that he wouldn't have normally chosen himself because I told him he could play Terraria if he reads the whole book (usually a short chapter book will buy him about an hour of screen time). Once the kids are sick of "earning" screen time, they find something else to do, like play outside, play with other toys, annoy me :), etc.
I do think screen time has a lot of benefits. I think my kids have learned a lot from games like Minecraft, Coolmath4kids, math and reading teaching websites (like ixl.com or Razkids.com), etc. They have also started researching things, like DS has been on the NASA website reading about space stations and rockets. He like the interactive features that you wouldn't get from a book.
