Thanks coderintherye, all very good points.
If I'm not mistaken Evernote had tens of millions of users.
I'd assume a note-taking app with a better UX has the potential to have at least the same ballpark. I think Evernote's mistake was raising too much money and not differentiating the product from competition...
That said, I really have no idea about conversion and monetization of such an app, because I couldn't find anything comparable.
Compared to Evernote, Remindful doesn't require you to manage your notes, can store complete documents and articles and answer questions about any part of the content.
Moreover, it would be able to actually remind you about important dates and things.
So far people I've spoken to said they need something like this, but at the moment the MVP is not quite ready to be able to charge for it...