I think the cutting costs and distractions are extremely important variables when even thinking about trying to quantify the benefit of remote workers. But of course your productivity drops when you're in the office when you're not usually. People are taking advantage of one of the few times you're on-site, increased distractions already. The environment you're working in on-site is no longer what you're used to working in. Meaning you don't put up with distractions as well as you would if you worked there every day. And your body doesn't really go into 'work-mode'.

It goes the same way for someone who works in the office every day then decides to work at home. When I've had a dedicated office space in my home and worked there for an extended time, I always feel like I missed out on some social aspects that I needed from the office environment, including both productive and unproductive communication, but my productivity went up. But now that I've been working daily in an office, and I do not have a dedicated space at home, when I do end up working from home, i'm far more distracted. I think it's easy to look at either side and flail your hands attempting to qualify as well as justify what you're doing. But it's not that cut and dry. In your experience working from home may make perfect sense, but I still don't think it's easy to quantify the benefit of remote workers. For a lot of people working remotely is distracting in a different way, and you end up giving up a lot of essential in-office interactions, sometimes without ever realizing it.