Sometimes I think I do not need to install Anki client software on each computer.
Just use ankiweb to browse the cards.
Perhaps AnkiWeb does not have the function to download shared decks and add media files. For students who cannot afford the paid AnkiMobile they typically create cards on their laptops and review them on the free AnkiWeb, so I think it will work only with AnkiWeb as you say if the decks are already there. (or if users do not use media files or shared decks)
A question and answer are always enough for a simple and diligent student who wish to learn