This approach has a problem. Not everything can be relegated to a fixed schedule. For example, I have a friend taking next week off to go eclipse watching. How is that accommodated with a mandatory week off every 8.
The eclipse happens at a fixed time; if your model of vacation is that employees are supposed to swap their randomly-scheduled vacations around to get the times they want, you'll immediately notice that there's much more demand than supply for vacation during the eclipse.
Why is that "not any better" than the model where everyone wants to take vacation, but they're not allowed? It seems like an obvious improvement, whether you decide to close for the week or not.
My guess is simply that you can trade vacation weeks with others, and that they fall back to the traditional system when that doesn't work: whole company shutdown during Christmas, and submit vacation request form at other times.
I imagine the main issue Europeans will notice is that a week is pretty short. They're used to real vacations 2-4 weeks long.
Imagine having to miss something you were really looking forward to, then spend the following week on enforced leave. It would get old fast.