Interesting perspective. The problem is what you're spending time online doing. If you're looking at cute cats or on facebook, it's likely you're wasting time. I would also bet that lots of time is spent procrastinating. On the flip side I find time away from the computer to be highly unproductive. It's good if you need time away to relax, but overall there's alot of time wasted drinking beer, socialising etc. It's all about balance and getting important stuff done.
On-computer and off-computer time are equally (un)productive. I like to spend a long time thinking about a problem without writing any code, then get it all out in one go as a foundation to build on; something like the Feynman Algorithm. And time spent socialising is only wasted if you don’t make the most of it. Like you said, it’s important to enjoy yourself and maintain a good work–life balance—otherwise you’ll just be unproductive and depressed.