they are very persistent buggers and breed like... rodents
I've heard the tail is particularly tasty and easy to skin and cook.
It is interesting that we see our infrastructure as 'valid' or correct, but the work these engineers (beavers) put in as a nuisance. In an ideal world, the benefits to local biodiversity and ecosystem health should be balanced with the cost of relocating roads when necessary.
Maybe part of the problem is that humans in North America are largely not hunting beavers anymore?
We're very capable of being the predators that keep animal populations in check, and plenty of people do still hunt, but I don't think I've ever heard of anyone hunting beavers in my life