I find this discussion very interesting. I have older stepkids who grew up with unlimited screen time at their mom's house (and also a lack of emphasis on school, which is reflected on report cards).
When DD was born, I guess I followed my instincts. It bothered me to see her spending too much time in front of a screen. It bothered me to see how addicting that stuff was to my stepkids.
I was raised in an era before home computer games (unless you count Pong). And there wasn't much kid programming on TV outside of Saturday mornings.
So I naturally tended to limit screen time for DD to Saturday mornings because it just felt more "right" to me (not an absolute rule, just sort of a general one). When DD asks to watch, I often suggest an alternative activity. As a result, when she was three, she designed her own unique handbags out of construction paper and wrote her first children's book. It was worth the boredom moments, in my opinion.
That said, she has a gifted classmate who appears to have unlimited screen time and it certainly has not slowed that kid down in any way intellectually. His journal writing assignments do tend to revolve around Mario, etc., instead of some more profound or social subjects, though, which makes me sigh a little.
On the other hand, my stepdaughter moved in with us 6 months ago and in that short time her grades have improved enormously. Part of that is due to the value we place on school, but I think living in our "boring" household with limited screen exposure helps, too.