It just evolved to be that way, I don't know of any single decision point where we said nope, done with paper. Obviously won't work for every type of organization, but I'm quite happy not having to deal with physical paper. Feels very... quaint.. to have to do so - like staying at a B&B without, say, electricity, where you must churn your own butter.
Now all that said, there is one huge downside to this type of office - everyone looks at their laptops or tablets in meetings. People are constantly distracted. I haven't been in a meeting in months where everyone is focused (though I can't say that was true of paperful offices either). Is it better/worse? I don't know, but if I had to pick between the two, I'd pick no paper every time.