I don�t disagree with any of the contributions above. But, the way you look at beavers, like everything else about your pond, depends on circumstances. My pond is about 90% surrounded by trees, and when the beavers kill some, there are plenty of others. I enclose the few trees which I specifically don't want to lose with a ring of hogwire. That seems enough to send them to other sources of bark.
Two of the lodges which were where when I bought the place in '92 are still active. They don't bother me, and I don't bother them (except when one slaps the water behind me and I nearly dive out of the boat). In fact, the lodges are "hot spots" for fishing because of the limbs and branches that the beaver have dropped in the water around them.
They do try to dam the spillway in winters with lots of overflow. All it takes to outsmart them is to pull down a foot or so of their dam with a hoe while it is still early. They will spend the next day or two rebuilding that and will not add to the rest of the dam or bring in any larger material until the damage is completely repaired with small sticks and mud. Then, I spend five minutes opening it back up again. I like the slight retardation of overflow because it raises the water a few inches, which makes for some good spots to cast at the bases of the swamp maples.
Now if the critters ever start tunneling in the dam, itself, they better pack their bags.
Good luck with keeping your pond "natural," and I hope you have a few lunkers in it, already.
Lou 13.5 acres