Pioneered in Maine btw! The fish seem to do just fine[0][1]. At the end of video I've linked you'll notice they'll dump them out after landing if possible.[2]
>Department biologists using scuba gear have had trout dropped around them and observed as the fish hit the water and swam away. The biologists report that most of the trout easily survive their aerial drop without injury or harm.[0]
>The Aviation Division also supports the bureau's resource management efforts through aerial fish stocking and various data collection efforts. Aerial stocking is the least stressful method of delivering live trout and salmon to inaccessible or distant locations, Maine's Warden Pilots release more than 182,000 of them — over 28,000 lbs. — into 195+ lakes and ponds each year.[1]
I suspect the program wouldn't last long once they realized the beavers would "come back". Not the same ones, but new ones to the same place they removed them from.
Beavers move too wherever they can find a 'good' spot to build a dam and lodge. If your back yard is such a spot, beavers will move in. As the article says, the right solution is to find ways to live with them.
In my childhood home, the big pond behind our house (maybe 200ft across?) existed because of a big beaver dam. Generations of beavers maintained it. We'd lose a tree or two occasionally, but well worth the benefits.
Why beavers make dams is very interesting - they tend to instinctively build at the site of the sound (beavers are nearly blind) of running water. Canadian wildlife management has used this knowledge to trick beavers into not building dams where it would be inconvenient for highway management.