Great words of wisdom from MotherofToddler.
On the topic of linking screen interests to the real world, I tend to sandwich screen time between analog activities reacting to the same topic. So, with our current "Dinosaur Train" obsession, we read dinosaur books before and after watching the show, or act out the show with figurines, to pre- and post-saturate DS in dinosaur activities.
I'm probably tilted more toward the laissez-faire end of the screen time spectrum. I let a previous "Winnie the Pooh" obsession play out naturally a few months ago and, even at its peak, we'd watch maybe 90 minutes of Pooh per day. (I didn't allow any other screen time.) The peak lasted a few days and fizzled to zero within a week when DS was left to indulge ad libitum. Most days, we have about a hour of screen time from all sources.
Now, if he wanted to read Pooh, draw the characters, build their homes, or act out the books, I'd let that go on all day. YMMV.
Back to the topic of reading: I've found a fun way to incorporate some physical play into learning to read (or anything) is jumping games. Draw words or letters on the driveway in chalk and run or jump from letter to letter to form words. You can race, compete for letter spaces, etc. It's how I taught DS to jump, incidentally.
