Was it Mario Paint that let you make music levels?
I wouldn't say levels, but you could make music..
You could also make animations but I barely see any of those (at least anything as wonderful as the music) on youtube. I wonder, is it because the animating tools weren't that good compared to the composition tools, or do people just suck? :P
Not that simple.
They would have to design a system where you can see other peoples levels, search all the levels made by a specific user and have a spot for featured levels that are enjoyable, for experts etc.
Then they would need some kind of cloud storage for it where you can upload a number of levels and people could download them.
A level designer is one thing but then there's all that other stuff behind it.
With any other company I'd agree with you. All those things you mentioned are absolutely essential for a level editor to have any real relevance. As this is Nintendo, however, I have a feeling that we're likely to see something much less auspicious should they decide to go ahead with this idea. We still don't have online multiplayer or proper leaderboards for the challenge modes in NSMB U for crying out loud (and I don't want to hear any excuses about how NSMB multiplayer can only be truely enjoyed locally).
While there is no excuse for them not adding it, I still think on-line multi for NSMB wouldn't feel the same and thus be less enjoyable. That is a personal opinion though.
****, I can't even enjoy local multiplayer if I'm not playing with the right people