They make my farm better. Somebody does have to go out regularly and take apart dams that threaten the road, but it is not hard to do if you never let the dams get high. If they do manage to back up a lot of water they get a lot more productive.
I looked into ‘beaver deceivers’ and similar things and decided to keep with a system that works. We have a tenant who does it for us, he has a great story to tell when he goes to any ‘new age’ gathering.
Already had a tractor axle broken, when the machine sinks with one wheel into the caves?
We got 50 € compensation and mentioned in the newspaper as "compensated" for the damage. This is a terraforming animal and not compatible with civilizations landscape, no matter what tales they tell.
A few years ago a beaver started taking some trees from the wetland-type area of the back part of our property.
It was pretty nice, actually.
But he went too far, of course, and there was flooding a little downstream of us (really not much more than a drainage creek though technically it connects two bodies of water and is optimistically titled a "river").
So he (or she, I don't know) was trapped, and the free landscaping ended.
Of course, it may have become a problem for me too, once I found my house in the middle of a new lake :)
I met someone who had beavers move into his farm in Iowa. He said that before it happened, he thought beavers were great. After getting to know them personally, he now thought of them as rats with chainsaws.
There is a family of beavers in the middle of Zurich that I occasionally visit at night. Their activity level is amazing, and pretty much every tree close to water within a mile of their habitat had to be ringed with a wire barrier (or was felled before the city got to it). I would not be surprised if they provided full time employment to a city employee or two.
But they've definitely managed to redecorate their living environment in interesting ways.
There are trees adapted to beaver activity. I haven't experienced this myself, but I've known a couple people who got real familiar with what trees can and which can't recover.
Willow is the king of chaotic waterways, sure, but lots of other trees can be coppiced, and coppice is basically what a beaver does to a tree.
A willow branch sticking out of a new sand-bar after a major storm can usually re-root itself. It has so much rooting hormone in it that you can use them to root other species. Some people take a bucket, fill it with cuttings mixed with some ratio of willow to leak hormone into the water and be taken up by the other branches.
There's a nice Nature episode on beavers and their interaction with people and the environment. It's titled "Leave it to Beavers" and you can find it in various places online.
Two of my kids had a 2nd-3rd grade teacher who spent a lot of time teaching about beavers, so they know all sorts of random beaver information. Their class mascot was a stuffed beaver named "Justin Beaver" :)
I looked into ‘beaver deceivers’ and similar things and decided to keep with a system that works. We have a tenant who does it for us, he has a great story to tell when he goes to any ‘new age’ gathering.