Android has a file system, but almost every app goes out of its way to hide that fact from you. I have almost no idea where any particular app is going to save files to, and so it's playing needle in a haystack every time I want to open a file created by one app in a different one.
This is another case where Apple didn't invent something, but made the best version of it.
For a device that didn't have a public file system until recently, the iPad's both works and makes sense. It's iPod, mobile phone, Bluetooth headphones all over again, on a feature level.