Sorry you feel that way, arsenix2001.
I doubt you'd be feeling the same way if you had over two dozen mature bearing blueberry bushes wiped out by them; and lost significant revenue because of it. Or had them wipe out half a stand of American Chestnuts being grown for resistance and restoration.
You see, chicken wire, chain-link fence, or even metal flashing has a pretty high failure rate against beavers. Just ask the National Park Service about the cherry trees along the Potomac River. The beavers either bit through the thin wires, or they climbed the **** things and chewed through just above them.
And trapping and relocation don't work anymore. The eastern seaboard beaver population is at saturation levels. Relocation just means over population in the dumping location. Which results in either beavers starving to death (yeah, real humane), or causing problems in that area (not exactly a good neighbor policy.)
Shooting or trapping them is a more efficient method of control for the season. You'll have to keep it up as they flow into the area to replace the ones taken; but that's a sustainable, renewable resource. Meat to eat, pelts to use, and the non-edible parts never last more than a couple of days due to crows and foxes scarfing them up.
Point taken on the shooting angle at rodents in the water, and what's behind them. Shotgun makes a mess of the pelt, but better chance of a hit, and almost no risk of a ricochet. Body shots with a .22 aren't usually effective, those critters are too big unless you get a heart or head hit; plus they ricochet too easily. .38/.357 stops them cold with a single hit, and you have to have a really shallow trajectory to get those to skip.