Wait, what? You'd need hundreds of thousands of "small ponds" in the woods to approximate a comparison with a human mega reservoir like Lake Mead and associated reservoirs. I don't really understand the comparison.
I think you're underestimating the extent of beaver altered terrain in the west. Estimates are between 60 and 400 million beaver before the fur trade started. We are currently sitting at 6-12 million and there are a number of watersheds where they have to be reintroduced because there are no populations in that area.
I was actually reading the other day about beavers and supposedly as much as 10% of North America was covered in beaver-built reservoirs and ponds. There were a lot of beavers.