Is there some reason why VE is not enabled in Wikiversity:Draft: space? It would be very useful to have it available there. I currently develop drafts in User: space for this reason. However I have noticed that conversely there are some display features which are available in Draft: space but not in User: space, in particular Reference tooltips work in Draft: but not in a User: page. I am working on a draft of a resource that employs many footnotes designed to be viewed quickly as mouse-fly-over Reference tooltips, but testing them in User: space isn't possible.
Topic on VisualEditor/Feedback
Well...
The answer to your direct question is that it doesn't work because it wasn't enabled, and that could be changed. Ideally, you (or someone) would hold an official discussion in which that community agrees that it would be a good idea, etc., and then we file a request in Phabricator. (Filing the request is easy; one of us just copies something like T126561 or T223024, and then we wait for either a volunteer or staff dev to process it. The point of the discussion is to prevent someone from adding a #community-consensus-needed tag, and thus getting the Phab task delayed.)
The thing I think you might want to consider is: Should Wikiversity have a Draft: space at all? The research I've heard about suggests that it's where pages go to die, and if you're serious about building content, it's much better to have that content in the mainspace. (This research was done by the same people who originally proposed Draft: space at the English Wikipedia, and they are no longer as enthusiastic as they used to be.)
Yes, I think you're right that perhaps the Wikiversity Draft: space isn't a good place to populate after all. Developing content in the Wikiversity mainspace solves both the problems I mentioned, because both VE and Reference tooltips work there. That said, there will still be drafts in User: space. Do you know why Reference tooltips don't work in User: space? I think I'd like to follow the discussion/request route you suggest to get that enabled (in WIkiversity:User:, not WIkipedia:User:), if there isn't some reason it shouldn't be.
I don't know why the Reference Tooltips feature doesn't work in userpsace. (Shouldn't it work everywhere?) If you're running the same gadget, then @Yair rand is probably the best person to ask.