Looks like normal SSL traffic to your IT department. Looks like the free and open internet to you. There are plenty of providers out there who will hook you up with a connection for $5-10/month, if you don't feel like setting up your own.
In my office, there are about a hundred employees and we rely on three printers which mostly sit idle. As a software development company, most of the things we are working on are digital to start with. I routinely go months without handling a piece of paper at work.
At home, there are still one or two things that come as paper mail, usually financial in nature. That gets scanned and shredded unless I'm required to keep it by law - tax documents for example. I have a three or four inch thick stack of legal and financial papers in my safe and that's all the paper in my life.
The paperless office is rare, perhaps, but quite possible.
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