One is adding something (school), the other is taking something away. Further it takes a leisure activity away which is (to your point) performed exclusively outside of school. A more pointed discussion that still allows the benefit of government policy is why mandate a limit rather than mandating a system that allows parents to usefully set the limit? A related discussion would be if I claimed that TV and fiction novels are worse for kids than games, so we should allow unlimited games but limit all fiction books and all TV to 3 hours a week for everyone.
Time can't be increased or decreased. You have 24 hours in a day, no more, no less. Adding something to the schedule is only more stringent than having a blocklist of activities where you'd at least have a choice.
I don't want to start an argument on the effect and difference of fiction books / tv to games. You point is effectively that those choices may be arbitrary, however games are much more addictive than those that you've mentioned. Realistically, I've seen kids play too much games whose grades dropped like hell, but few watching too much TV, much less reading too much novel. Games can be addictive and difficult to maintain, while the same can hardly be said to TV and novels.
I agree that government-mandated limit would be too much, and less preferrable than a government-mandated system that allows parent to set the limit. You would effectively be requiring game companies to acquire and collect information on the parents of the child playing the game.
I expect a government-mandated default unless with explicit written approval from parents which would seems still rather easy to circumvent for the lack of better ways.
