Example of currently existing system
Pros
Addiction prevention
As of now it has became apparent and proven that gaming can cause an addiction. Most addictive substances or activities that we know of are currently limited under legal age restrictions, such as gambling, sex or alcohol. It has also been proven that children and teens are more prone to addiction than adults. With those facts in mind, it would be logical to limit most games in order to protect children from possibility of early addiction
Fair gameplay
Many kids can be found playing very competitive games, such as League of Legends, CS:GO, PUBG just to name a few and most of these games require team cooperation in order to succeed. Most kids tend to be incapable of keeping up with competitive gameplay, so more than often they can cost a win to the rest of the team.
If those games were legally limited by certain age rating, competitive gameplay would be more fair and balanced.
There are many things that can harm or cause addiction in children yet are available to them legally such as junk food and television. Parenting is a subjective matter and the decision to allow a child to play certain games should be at a parent's discretion.
Oh come on are we going to start fining or punishing parents because we don't like playing games with kids on our team? Sure it sucks but say one nation does start doing that, you'll still have to deal with the other nation's kids.
The fact that in most countries a 10 year old kid can walk into a shop and buy Outlast or The Witcher is ridiculous considering how much control there is on other potentially harmful media and substances.
Or you could not neglet your kids instead. Whether or not I think your child should be playing postal is not important, if they're playing videogames you don't want them to it's most likely your fault for giving them money to buy them or leaving them unattended with the 21st century electronic babysitter that they used to download it.
Punishments
Minors can't be punished by law, so it would have to target sellers or parents. This would put unnecessary stress on both parties, because now parents would be paranoid that their kid is playing games "illegally", and game markets would have to ID buyers, adding extra step to every sale.