That's fine when everyone everywhere uses the same OS or all OSs automatically connect to the same back end. But if I want to share files between a Windows box, an iPad, and an Android phone, it's unlikely that anything useful for my purposes will be built into the OS anytime soon.
And even if I insist on buying nothing but Apple (or whatever) products, if I want to share files with my dad or my next door neighbor, now I have to worry about what OS they're running too.
You install Dropbox once per device. After that, it's trivially easy.