It’s fair to say that many kids feel like they have little power over the world around them. From a young age, parents and teachers introduce them to the idea of power through media such as film and books, but also though the interchange between adults that kids watch around them. For some kids, school can be a place where they feel relatively powerless. The day is pre organised by a teacher (who did a deal with parents to get them dropped off daily). The things they learn about are directed by teachers, and the rules about what you can and can’t do are upheld by the teacher. You can choose to ‘fail’ or mess about, but generally speaking, teachers gang up with parents and the end result is even less power.
If however you are given access to virtual spaces where you can build up a sense of power (being good a your favourite game) then it makes perfect sense to want to tap into that feeling when you have had some gut-wrenching experience where someone has used their power to smash your confidence or to further erode your reputation with your immediate peers. If you’re lucky, you’ll have “best friends” who support you – but even such cases, most kids have to work very hard at maintaining those relationships – and it’s even harder to do when you feel more powerless than usual. You might have flunked a test, become the target of some kids smart-ass remarks today, fallen over to the amusement of others … there is an in-exhaustible number of things that reduce a kids perception of their power and confidence in school – or at home.
So if your child is feeling a little powerless, they might not tell you. They might not even know themselves. You might look at their patterns of play. You might notice their changing interest in their choice of games. You might notice they change the kind of class they play. They might start getting into more ‘risky’ situations … they are probably seeking to get back some of that power-drain.
Kicking them off the computer for playing “too much” might inhibit some of their need to ‘take back some power’ at the very time they are needing some. I’m not suggesting games solve issues of power, but they do help kids work though some fairly difficult problems when they can’t ‘see’ other ways to do them. Each era has media that speaks to kids, whether its Marlon Brando, James Dean, The Breakfast Club or Buffy, there have been media that kids have found some empathy with.
Parents struggle to deal with boy-power and girl-power, so I’m not suggesting games are a surrogate or are something to allow in the hope that kids who are anxious will ‘snap out of it’. What they are looking for are ways to build up their self-efficacy and confidence as the world opens up to them. A badge won’t do that. They need to find meaningful work.
Some teachers clearly know how to do this, and some don’t. Same with parents. But don’t hate Minecraft because they like to play it so much, just consider how powerful they are in the game – and ask yourself, if they feel that good all the time? It might just lead you to discover something you didn’t know about them and how they feel.
If you can’t hear or see joy when they play, do not try to measure the hours played in order to rationalize it. Check their happiness meter, your kid might need a power up in some other way. That’s where the parenting wisdom comes in.
Playable 
I agree with much of what you say here. Power is as much emotional as it is about identity and socialisation. In a dominant adult/teacher/parent world, children form group codes and languages, secret places and membership systems. This translates easily into multiplayer games. The fun (emotion) in well-designed games can embody novelty, challenges, friendships and meaning wrapped in a story.