> ...For example, maybe Unis get together to publish their own wikis on more academic subjects. ...
There's nothing stopping them from doing this. Wikis are actually a nice example of a federated standard, with good support for "InterWiki" cross-linking, well-understood naming conventions (thanks to Wikipedia) for encyclopedia-like articles, and open licensing via CC-BY-SA.
As the top commenter noted, there are problems.
Though it would be sad if a commercial entity put Wikipedia 'out of business' per say, I think 'more variety' in this space would be welcome.
I'd have no problem looking to different sources for a more authoritative source of information.
For example, maybe Unis get together to publish their own wikis on more academic subjects. Maybe companies can have a Wiki to make their own articles about their own articles (I understand they have web sites for that, but the Wiki format is different).
More variety would generally be better not worse.