Are those of us without DC at Top Academic Independent School allowed to voice opinion?? 
OP I do think your title rather snobbily implies that of course this is not an issue for children at Ordinary Schools since they never get any homework/do extra-curricular anyway; heavens darling! They probably spend most of the school day on games consoles! 
Right, having got that off chest ..I have DS in Y7 and have gone on a bit of a journey with this screen time thing (as in so many other areas tbh).
Few years back I would definitely have agreed with the earlier posters here; Just Remove it, Be a Parent, No screens during the week, All tasks completed first (best of all never get a console at all etc etc.) And indeed, when DS was younger I did take a pretty firm line. But distracting him - with trip to park, train set etc- was fairly easy (and cheap) then, plus what he wanted to do on screen - basically CBeebies plus - much more limited.
Like you OP I would have considered just about Anything- reading (of course) but also sport, any kind of playing out, Lego, messy or soft play - a preferable use of his time. And there’s still little doubt in my mind that unlimited screen time from early age will negatively impact most boys’ inclination to pick up a book or anything else. You have to turn it off to get results, obvs . . Especially when they are little.
However when it comes to prepubescent gaming obsession I have come round to the views expressed by sethis, goodbyestranger .. . Much teenage gaming may be mindless violence but the more I engage myself the more I can see that an awful lot of it is much more than that. But even if it were . . To be able to work hard at school kids really do need (mindless) downtime at home!
Plus there’s the self-regulation point . . learning to take responsibility for own progress is a huge part of what secondary school is about imo. They can’t do that without being granted some freedom to abuse!
So here’s what we do:
DS gets home anytime between 4 and 6 depending on extra-curricular . . Straight off, he’ll (demand food and) start gaming . . I have mixed feelings, part of me would like him to work first, but I agree with goodbyestranger that it is a part of winding down/chilling out. Before hour is up - earlier if already 6 - he’ll have explained to me what he has to do this evening and when he reckons it is happening. And on the whole, it does. . Frequently between tasks he’ll give himself another little gaming holiday but (with my help) keeps his eye on that clock. It’s my only fixed rule; all homework, practice and screens done by 8pm.
My hope/anticipation is that fairly soon I won’t need to check schedule at all, can just trust him to get on with it by himself . . He’ll get more homework, probably, but I work on assumption that he wants to do well at school, do it adequately and on time. All he needs help with at this stage is scheduling.
From this school year he has had a computer in his bedroom- another former resolution of mine up the spout. But it is used for homework as much as gaming, during term time anyway.
So that’s it, all subject to review as the years pass. Finally, I have to ask myself. . I grew up with virtually no screens at all, even reception of the very few tv channels available then (early 1970s) was touch and go where we lived . . And yes I did become fairly voracious reader, as I still am. But do I think kids today dimmer, less creative, less clued up intellectually emotionally and every other way than we were at the same age? No, no, and absolutely not. On the contrary, the ones I know would have left us standing, mouths agape . .