The answer is, it depends
I noticed that the MSDN wiki for Visual Studio has just three markup tags for content edits. It appears you get basically three tags: heading, body, and code. Now, in their case, they have strictly defined what they intend for users to enter in their wiki, which is intended to contain mostly code snippets that support the reference documentation. I believe limiting the tag set helps when the intended content is narrowly defined.
At the opposite end of the spectrum, my thoughts on a DITA Wiki tool would allow for many many tags to be used, in fact, all the tags that DITA allows could be used in a DITA-based Wiki. Would this freedom to tag cause fewer people to contribute? Or would the contributions be all the richer and fuller due to the ability to write just what you need to for that particular topic? Let me know what you think.