A few times we got "work from home" day when teams moved from one building to another. You would expect more emails that day than usual as you could not just talk in person. Well, both number of email and commits went down significantly which tells me that people mostly "worked" from home that day.
That was a one-off event. Folks who don't regularly remote work will think of that as a "treat". In their minds they're probably viewing it as an unofficial day off.
Assuming that's comparable to a true remote work policy is silly.
If you're measuring productivity by email and commit volume, and you're a manager, you should be fired. It's the digital equivalent of "hours in the chair".
Personally, I can't effectively work at home. If you send me home to work, I'm going to be constantly distracted. If you want me to be productive, make sure I have an office.
So, with forewarning, I'm not the only person like this, and if a manager or executive wants to make this kind of decision and expect productivity to not suffer, they're being... stupid.