There are so many factors that influence child development and media use. I don't think it is even possible to properly control for them.

How can you for example control for the believe that they are bad? Better parents will have more success reducing the metrics that are believed to be bad than other parents. How can you control for the rising philosophy?

I'm especially skeptical about the claim about ADHD and that games are bad. There is lots of evidence that games, especially of competitive nature like shooters or strategy games, improve cognitive functions. ADHD is to a large degree heritable and influences all kinds of behavior. I think it is by far more realistic that ADHD would influence screen use and not the other way around.

Actually games improve very specialized cognitive functions. For instance you know that being good at chess doesn't relate much to being good at poker, and being good at tennis doesn't do much for your football abilities.

Similarly, being good at some FPS game makes you at best marginally better at video games of a different genre, and have no actual relationship to your abilities in the real world. Even a study on driving games showed no improvement of actual driving in test subjects.