Do you have any understanding of how sedating drugs work? For starters, you have to have a vet present every time they are used to estimate the weight of the animal and then determine the amount of drug to be used. And if they are wrong either the animal dies or it is not sedated. And you need a team to quickly trailer the animal and remove it before it wakes up.
This is not practical when you have a handful of deputies trying to catch 50 large animals while night is approaching. Not to mention the logistics of gathering up enough sedatives to put down dozens of big cats and bears at a moments notice.
Sure it sounds good, but it's about as unrealistic as wanting the cops to shoot badguys' guns out of their hands.
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