It's not like Nintendo doesn't allow it. Third-party developers just don't want to make more games for the Wii (U). In the WiiU's case hardware sales have been so low that they fear for their profit, they're afraid of their game not selling enough because too few people actually own a console. In addition to that you can't simply port any game you've made for other consoles such as the PS3/4 because the tablet controller requires extra effort (= time and money).
The Wii surely won't get an official Minecraft version. However, there have been attempts to create a Minecraft clone for hacked Wiis that could load worlds from PC based servers. Unfortunately this project has been abandoned about a year ago, and remained only partially functional since.
In regards to a WiiU version of Minecraft: As many people stated before me Mojang wouldn't mind creating it but they have too much work on their hands. They may get on it after they finally finish their mod API (MC v1.9? v1.10?), at which point WiiU sales should have gone up as well. 2014 should prove to be a successful year for Nintendo's console as many popular games such as Mario Kart 8, Smash Bros., Bayonetta 2 and Xenoblade 2 will all be launched this year which will surely boost hardware sales.
TL;DR
Mojang won't develop a Wii version as that console is out of date. A WiiU version is very well possible, though likely not in the near future.
