We have most of that today, and I certainly would not call the present day US a religious society. For the average person on the street, gods and their worship plays a very small role in their day-to-day lives now as it did then. Anthropological accounts of the time give the impression that deference to the gods was more rote than pious. Now, if we expand “religion” to include things not relating to divinity, then we most certainly are religious today. Our religion just goes by names like “liberalism” and “progress”. And since the birth of the Westphalian nation-state, the nation itself has become something of a deity.

One problem with this discussion is that the originator has defined the terms so narrowly, that I can’t see that what he’s referring to has ever existed in the first place, let alone succeeded. And as you point out, the measures of this “success” are themselves open to interpretation.