First, if you have a pond beavers will come over at night and dig holes the width of a basketball about a meter from the edge of the pond into the water (vertically down, then sideways). They camouflage these holes or they simply overgrow, good luck to an unsuspecting human that had his/her leg fall into such a deep hole.
Then, they dig such holes and passages into earthworks designed as flood defenses. Huge amount of money goes into fixing such earthworks.
Finally, if you(or anyone nearby) happen to have drainage channels or small rivers, these will be blocked by beavers to the point of flooding the surrounding area. Various compensation schemes exist, but not everyone has documentation to use them.
Fibally,a braver can be a very dangerous animal when startled/provoked/cornered. Around here every person is told in their youth, "don't approach beavers" or if they bite you in the leg (usually groin area) you'll bled out in 20s.
No, beavers are not nice... If course they shouldn't be eradicated, but they should be managed properly, not enjoy 100% protection as they do here in Poland, for example.