Beavers create plenty of problems, which require significant control.
They tend to block culverts and drains in often successful attempts to make ponds.
The ponds then flood roads and other areas.
That was the old days, now everybody will ooh and awe as the flood waters wash away the feces.
They will destroy a good trout stream in a blink.
There are some who run to the beaver ponds on trout streams since the brookies get big. But after a couple years, there aint any more fish. The ponds cover up the prime spawning sites with silt.
You are correct. And California banned animal trapping a couple of years ago. They are getting over run with beaver and coyote because there is no control of the populations.