Anyone uses IMAP email? Works just fine (save for IMAP design but that's another story).
Same with CalDAV.
For stydy I use Anki and it has brilliant sync (it can even automatically/automagaically merge study changes when I study some items on mobile and others on desktop).
Many seem to claim that it's impossible to sync correctly in "colaborative environment" as in it would always involved dozens of people constantly working and editing the document (which would be utterly difficult to track the evolution of)… Most of the time it's not that colaborative and having the data locally makes it easier to work with.
OTOH not everything has to be (web-)app…