I agree. I am not sure it is as similar to sleep as you claim, but its definitely good for your brain.
I say something similar in the context of parenting, that a reasonable amount of boredom is good. I think it likely that being constantly entertained makes people more prone to seek constant stimulation.
This did not start with phones either. I am Gen X and it happened in my childhood with kids being dumped in front of TVs. One difference was a lot of adults resisted this and limited hours in front of a TV, whereas now a lot of adults are addicted to phones too.
I highly recommend road-tripping to those that can. At least once a year I end up driving out from the Mid-Waste to the Bay Area or SoCal. A few years ago the wife and I traded duties to drive to various parts of Alaska and back.
We've spent a week or so exploring just one state at a time…
There's nothing so mentally refreshing as a long, boring drive.
Well I made no claim of it being related to sleep; just that I've read a lot of claims that it's related to microsleep and used "sleeping while standing up" for the last bit as an analogy.
I am not a sleep doctor/therapist nor am I any sort of expert on the subject.
I remember when cable TV used to be "addictive". Now I can't watch even 10 minutes of it without getting bored and pulling out my phone. Also something I learned recently: checking your phone at the movies is no longer the faux pas that it used to be.
There's definitely some hedonic treadmill type thing going on with attention and stimuli.