You can deny your enemies from getting the food or population bonus from barbarian attacks by defeating them by yourself. However you can't seem to cause the enemy civ lose population by engaging barbarians forces and then retreating.
if people try that it should shift to attack them instead... with no bonus available
I find denying a bonus to a single team member of an opponent team that occurs roughly once every day or so is not much of a strategy. I guess it slows them down slightly but I enjoy finding more creative and devastating ways to overcome them
I find them all and do them all. If it hurts them it hurts them and then it's worth doing.