That argument falls down when one can point to a very well-maintained wiki hosted elsewhere. If the Star Trek wiki is well-maintained where it is, then it seems reasonable to assume that if were wholly incorporated within Wikipedia, it would be just as well maintained there.
The one from the Final Fantasy Wiki is from the perspective of a Final Fantasy fan, and is generally for a Final Fantasy fan. That is, it's explaining how Aerith relates to the rest of Final Fantasy. Some of it flirts with being in-fiction.
The Wikipedia article is more about how Aerith the fictional character relates to the real world. My point is that the people who want to maintain the versions that are more in-fiction may not also want to maintain versions that are more focused to how this fictional thing relates to the real world.
That argument works well with the Star Trek wiki as example. I don't think it goes as well with the Minecraft wiki.
Fan wikis like this are targeted at people that already have a fairly good understanding of what the article is about. This allows them to ignore certain aspects and assume a lot of things are already known.
In case of Wikipedia you have to assume much less prior knowledge and you have to start at the very beginning with each article. If you're already in the know, this gets boring very quickly.
This means that there is always going to be a space for separate wikis that cover specialized topics in detail for a different audience.
There is something to be said for different communities with differing standards or technical tools, and some separation from Wikipedia might be a good idea. Wikipedia has different projects for different topics, but in the end many decisions and guidelines apply globally.
Also for legal reasons, many fan wikis by necessity include a lot of detail about and data from copyrighted franchises that wikipedia might not want to touch (Screencaps, audio snippets, ...).
It would be nice if there were a set of reliable hosts and a standard for inter-wiki linking there, though. Prominently direct readers to reliable pokemon/Fallout/StarTrek wikis for details.
