Anecdotal evidence, but I sat very close to TV screens and handheld devices as a child and I am the only member of my family that had massive damage to my eyesight. I was 20/20 as a kid, 20/60 later and had as bad as 20/250 (nearsighted) before surgery. My eyes had stabalized at that point which is why I was allowed to get the surgery. Now I am 20/20 again after surgery. My entire family is 20/20 while I was nearsighted. I believe my eye strain sitting so close to the TV and gameboy made my cornea grow more than normal. Most people believe your eyes are finished at birth, but this is not true. Your cornea/eyes change shape into your mid 20s, and while overall changes are usually small they can make dramatic affects to your overall eye performance.
Eyesight has gotten worse the last couple decades, with nearsightedness dramatically increaseing which would lead me to beleive the heavy increase of screen use do have an effect. Objectively, most doctors say they just cause strain and not long term affects, but I just don't agree. Perhaps this is too new a phenomenom to even really properly test being that tablets and such have only really existed in mainstream for a solid decade or two. My two cents.
I am not trying to fear monger and I would say that its use is fine as long as they exercise their eyes in other ways and aren't playing games for 5-6 hours a day like I was as a kid.
