I have never worked from home so I don't know anything for certain, but I find it hard to believe that anything could be less productive than an office setting. I worked in the field and was almost never in the office. We worked hard and steady all day. We took no breaks, not even for lunch, which was unpaid and frequently worked past quitting time with no pay. That was mostly just the culture of the job but there were also practical reasons for it. Then I had major surgery and had to spend five months in the office on light duty.
I was shocked at how little work anybody actually did in that office. Especially since I could never consider sitting in a meeting picking my nose and doodling on a piece of paper to be constructive in anyway. It took me about three weeks to fall completely into office slug mode and understand how an office setting can suck the life and ambition out of anyone's soul.