The amount of potential creativeness and ingenuity that exists just in vanilla-minecraft makes the game more appealing developmentally to kids. Building structures develops spacial reasoning and 3d thinking. Collecting resources disciplines management skills. Collaborating with others and respecting their buildings both teach important social behaviors that are otherwise non-existent in most other popular games. These are just a few reasons why minecraft is both a really fun game, and a really exciting game to push further.
It's the modern sandbox game, and it's just a canvas. So we are trying to bring programming to the above skill set with learntomod.
It's fun and relaxing, and there's some evidence that children need relaxation.
It's also potentially sociable, if you can find a suitable server.
While I wouldn't want to overstate the benefits of Minecraft I do think it's a pretty awesome game that changes to fit the playstyle of whoever's using it.
I've seen amazing things made in creative. Not just stuff turned into a model and imported, but built block by block.
> I dared not to let them play as I was told it's too addictive for kids...
Set firm boundaries and stick to them. Set conditions on play - "You must have finished homework before play". This also means that you have a privilege that you can withdraw if needed.
The client costs $26.95; you can buy it online with a credit card, or buy prepaid game license cards in some stores. You authenticate with Mojang's central server when you play the game. Actual game servers are usually configured to reject client connections if the user isn't authenticated. (You can turn that option off, but you get a big warning message in the server logs when you do.)
The same login for "vanilla" Minecraft also works with modded versions, such as those accessed through the Technic Launcher (http://www.technicpack.net).
My server is actually at my home, so my godsons and their mother use a VPN to log into it. It's easier to have it hosted on a cloud service like DO. (If you're just accessing it at home, you don't have to bother with the VPN part.)
While I myself can appreciate maintaining a linux VPS and installing things from scratch (erm, that's precisely how I do minecraft hosting), managed hosting 'just works' without a maintenance overhead, and there are easy to use web control panels for plugin installation and configuration.
Most servers that kids like to play on aren't standard - they are 3rd party modifications (ex: bukkit). Such 3rd party servers have plugins that make the gameplay more usable. Example of some useful plugins are essentials, worldedit, worldguard. The headaches you will typically get is upgrading the server (after a minecraft update) and installing plugins. The hosting services mentioned above make it incredibly easy.
The server is cheap enough, and if I wasn't so nuts it could handle a small number of players easily.
I don't know that minecraft needs to be beneficial. I certainly doubt super mario or sonic the hedgehog were when I was young. It's a game. It allows lots of creativity, it has lots of variety. No mod will change the fact that it's still a computer game. Treat it as such and I don't see a problem?