You can. You just have to make a strong enough argument to prove video games cause violence for a judge to let the case proceed. There's a reason it doesn't matter and it's not because video games are beyond banning.
Why not give people both the freedom and personal responsibility instead of making assigning parental duties to the government like China has recently?
Agreed. It should be applied to all services which are optimized for addiction. Social media is just the worst of the bunch due to its built in peer pressure.
You could argue that reading is addictive, maybe some people find math so as well. I became addicted to computers when I was a kid and we didn't even have the internet. Sports can be addictive, along with dancing, or just plain socializing. Silly, yes, but you can bet that there'd be lawsuits claiming all sorts of things are addictive and some number will find sympathetic juries. Seems like a pretty bad idea to me.