Here are some articles found online that shed light on parent issues with, and perspectives on, Minecraft.

Me, my son and Minecraft by Jane Costello
A reflection on a parents role & perspective on Minecraft In this case the parents were not yet prepared to allow their child to step into the multiplayer game, but certainly do recognize the value of play.

10 Problems That Parents Can Have With Minecraft by Bec Oakley
Lots of practical and salient advice in this post! It is well written and thoughtful and offers ways parents can overcome or address concerns. But these are not quick fixes they will involve playing with your kids, counseling, mentoring and scaffolding their play. As Bec concludes... "But there's really no getting around the fact that it's a game that requires parents to be involved if they want the experience to go smoothly for their kids. So if you don't want to do that - if you can't bring yourself to learn about the game or put in the time to supervise, sort out problems, keep them safe on multiplayer servers and prevent their obsession from becoming unhealthy - then Minecraft isn't the right game for your family."

Guess What, Parents? Minecraft Actually Teaches Your Kids These Skills to Succeed in Life.

It's not all fun and games.Margaret Rock in Modern Parent
This is a sound entry description of Minecraft and the kinds of skills and dispositions kids are learning through their play. As Margaret says, "The mystery of Minecraft’s near-hypnotic effect boils down its flexibility, engagement and community. Like most things, it can be taken to extremes. But overall, kids strategize, plan and connect with one another, learning how to set goals and work together to complete a task. Not that they would say so in those words, though."

Commonsense Media parent member reviews for Minecraft (dating from 2011 to today)
Some very interesting supportive and critical amassed comments and questions from techno-literate parents of children and youth players.