It's not impossible if it's predominantly automated. You have swarms of "police drones" on patrol actively scanning for other drones and when they see one that they don't like (some sort of signed certificate that authenticates the owner and their license) they shoot it down. It works as long as the "police drones" are plentiful and well dispersed to the point of maintaining dominance.
>and creating a total surveillance state as a by-product
that's what i meant when i said this brings its own host of problems. My point's not that our way of life will continue unabated my point is that this particular force multiplier goes both ways, and the defense will be a sort of "drone police corps". The biggest problems will be whatever happens outside of the "margin of error" (ie accidentally shooting down the wrong drones, civilians caught in crossfire, people hurt by falling debris) and the general end of any notion of privacy (not that America isn't already going in that direction anyways).
You're aware that the (to my knowledge, which is entirely based on documentaries) primary way drugs are shipped to the USA are drones nowadays? Some via air, some underwater etc
There is just to much area and drones are tiny. It's infeasible to track them without spending insane amounts of money (and creating a total surveillance state as a by-product)