There's definitely evidence that we're getting less and less physically fit as a population:
https://www.menshealth.com/health/a19525386/why-your-vision-...
https://www.stateofobesity.org/childhood-obesity-trends/
https://www.npr.org/sections/health-shots/2016/06/13/4815909...
Physical activity is in decline:
http://www.phitamerica.org/News_Archive/Says_Says_19-Year-Ol...
Less physical activity is also correlated with worse cognitive functioning:
https://www.ncbi.nlm.nih.gov/pubmed/27182986
Of course that's not a direct link to "screen time", but then what else could be drawing people to less and less physical activity? I doubt it is books or board games. It's a known fact that many modern apps/games are engineered to be addictive, exploiting loss aversion and reward mechanisms of the human brain.