I have been working on computers for close to 25 years now.  I sit in front of four screens every day and I have had no ill effects from it.  I think the fact that newer monitors have less of a refresh rate issue is probably a good thing.

With old CRT monitors the refresh rate could cause a rolling or flickering that was hard for some people to see, but it was there none the less.  It would constantly cause your eyes to focus and refocus.  

The advent of LCD's and LED's has made that much less of an issue.  While not totally clear the readability of today's monitors puts much less stress on your eyes and the muscles that control them.

As I said, I sit in front of a computer every day for close to 8 hours.  I also visit the eye doctor every year and I have had perfect vision since I was a kid.  Everyone else in my family wears glasses, but I am over 40 years old and have never needed glasses.

I think that speaks for itself as to how much screen time can impact your eyesight.