At what age did your kid start getting into videogames to the point he started playing games himself if you don't mind me asking? I have a 3.5 year old (and 1.5 year old) who has played Mario Kart with me here and there but I'm always weary of letting him play too much to the point he's always asking to play it.
I believe he started playing games himself around 5.5 year old?
I think we bought the Switch when he was around 5 year old. The console was originally intended to be used by me and my wife. We wanted to play Mario Party and Mario Kart 8 together. Later on, I picked up New Super Mario Bros. U Deluxe, Let's Go Pikachu/Eevee.
When he was 5 year old, I figured it would be fun to play Mario Party and Mario Kart with him. I also picked up 1-2-3 Switch and Arms. He didn't like them. He quickly became accustomed to the joy cons, the problem was he didn't like the stress of playing competitive games. He's was also a sore loser. Since he liked playing Lego and build things, I purchased Mario Maker 2, Lego Undercover, Animal Crossing and Stardew Valley. He loved it!
Then I figured: "he can exercise in front of the tv!" so I bought Ring Fit Adventure and Let's Dance.
From that moment on our Switch collection grew exponentially. I sometimes buy games without my wife knowing. Yeah, that's bad. I usually buy the games second-hand though (still bad, I know).
I understand your hesitance of letting your kid sit in front of the tv and play videogames (instead of, for example, accompanying him to go outside and play) and frustration or worry when he keeps on asking for it.
We tell him to
always (and I really mean: always) turn on the lights of the living room when playing games, always sit on a distance (on the couch) and take breaks in between to let his eyes rest and relax.
We encourage him to invite friends or go to a friend's house, to play outside when sunny, jump on the trampoline (we have an outdoor trampoline in the back garden as well as a small indoor trampoline in the living room), play sports (he has football practise twice a week now and occasionally football matches on Saturdays, swimming, running).
When he wakes up he plays like maybe 10 minutes on the Switch before going to school and maybe 1 hour to 1.5 hours in total before and after dinner. It really depends if he was busy that day (sports, friends etc.) and in what mood he is in. Some days he doesn't even touch the Switch.
Instead of playing games he watches tv, drawing a picture, crafting something.
We don't have screentime no. When he was 5/6 year old, we limited the screen use of the Switch, now not so much.
I have friends who let their kids play games or watch YouTube etc. on the parent's phones and iPads. Their faces are almost glued to the screen, there is no distance between the kid and the device. I have no facts regarding nearsightedness and farsightedness, I think sitting far away from the screen is still better to the child's eyes. (btw, I also feel watching tv in the dark and playing games in the dark are bad for your eyes, that's why we always turn on the lights.) I also read research articles that noted there is no correlation between near/farsightedness and screen distance, I'm not sure if I believe that. I do believe that eyes need rests and the need to "exercise and move" the eye muscles by looking far away and looking up close.
Anyway, some parents rather let a child read a book, but then the child is also reading up close. Further more, playing games actively stimulates a child's creativity and also helps them to read. We also frequently test his eyesight, just in case. He's a bright kid, but if we find out that his school grades are declining or his development stagnates then my wife will definitely take proper action.
What I want to say is, do what you think feels right. In our household this works, there will always be parents who will criticize our parenting.