Whether it's an environmental improvement depends on what your employees do on the day off. Less will be attributable to the company, but it's a giant leap to say this means it's better for the planet.

I like the references for 1-3, even if they might be cherry-picked it's still more likely to be signal than noise, but the rest seems like leaps and assumptions. There are very few companies where everyone wants to work 4 days, let alone have that day not be flexible, so closing the office for a day seems out of reach for all but the smallest businesses. Retention I'm also not so sure about, virtually every company in our line of work supports 36 or 32 hours per week and they virtually all pay proportional to hours so that's all same same.