It's been possible for a long time.

For antipersonnel use, guns are perfectly adequate and guns on tracking turrets have been widely deployed (for example, CIWS). The underlying technology is a ballistic calculator and a fast panning turret. Modern ballistic calculators, weather stations (a small device about the size of a cellphone), and good quality ammunition allows for incredible precision with small arms -- hitting something 25cm in diameter at 1000m is something people can do with these tools.

A weapon like this can't really "mass kill" -- it is for point targets -- but we have long had tools that can automatically track and kill. Why don't we employ them to shoot at people? We have the tagging technology, &c, as you mention.

One reason is that positive identification really does matter a lot when designing and developing weapon systems that automatically attack something.

The anti-missile use case is one of the most widespread uses for automatically targeted weapons in part because a missile is easily distinguished from other things that should not be killed: it is small, extremely hot, moves extremely fast, generally up in the air and moves towards the defense system. It is not a bird, a person, or even a friendly aircraft. The worst mistake the targeting system can make is shooting down a friendly missile. If a friendly missile is coming at you, maybe you need to shoot it down anyways...

Drones have a different signature from a missile and recognizing them in a way that doesn't confuse them with a bird, a balloon, &c, is different from recognizing missiles -- but here again, the worse thing that happens is you shoot down a friendly drone.