A lot of people have had that idea over the years (remember John Gage's "the network is the computer"?) You could even argue The Shockwave Rider, a 1975 Science Fiction novel, described it pretty well.
I don't know about the Steve Jobs quote though, do you have a link?
Technology-wise it was a bit of a dead end. However the underlying protocol was VNC which they invented for this purpose.
We don't have the infrastructure for this yet.
The absolutely open version - even if it was just storing apps centrally and downloading them on demand, and not downloading everything - would still require something like 100 times more bandwidth than we have now to be usably fast.
A workable version, with local storage providing device accounts for a small number of users, would still need more local storage than we have now, and storage isn't cheap enough yet to make this fully affordable.
256/512GB devices could possibly handle family needs, just about, but would struggle at work.
[1] via sshfs