I hate beavers more than hippies, yankees and commies......I've met hippies, yankees and commies that I liked. Never met a beaver that I liked. I kill them whenever I get the chance. Year round.
They have done a staggering amount of damage to my property. I don't even count the hundreds, if not thousands of young pines they've killed. In my most beautiful valley they killed well over 50 hardwood trees all of which were about as big around as two men reaching around. All they did was eat about a 6 inch ring all the way around them. What an incredible waste!
So like others here I feed them lead and steel without mercy. And in general that's not the kind of guy I am (I don't even shoot coyotes). In fact, when they first arrived my Dad wanted to trap them. I thought it was kind of nice to have them there. So naive. So stupid.
As for the pools that they make attracting dragon flies....well I think you might be missing piece of that eco-system puzzle. The pools attract and breed mosquitoes. The mosquitoes attract the dragon flies. The dragon flies cannot make a sizeable dent in the mosquitoes. Therefore: beavers = mosquitoes.
Hate to sound like a grumpy old man but having experienced the loss of beauty, value and income because of beavers I have no soft spot for them in my heart. No other species that I know (other than man) of causes that degree of destruction beyond its survival requirements as the beaver. I would be happy to keep my fire ants, kudzu and coyotes if I could lose the beaver in the deal!