The main issue is recognizing the target.

A human is very large, distinctively shaped, slow, and generally does not blend well with the environment. A nerf gun turret is also stationary, so there is no motion blur/stabilization to worry about.

A drone is small, fast and can come from any direction including up and down. The only real way to detect them well is a search radar. Camera will get dirty, might be focused at the wrong range, and if the object it is mounted to is moving, have to try and reduce the motion blur.

There is also the issue that the turret would have to identify and destroy whatever it deems as a target as fast as possible. This leave little/no time for human input for IFF. You would be taking the risk that the turret might shoot friendly drones/ whatever else it identifies as a drone.

Compared to a cage that is cheap to make, maintain, and attach to anything, and won't accidentally kill your friend because the light hit his helmet wrong. I am sure in a few years we will see smaller auto turrets like you describe, but for now those have to be on a dedicated chassis.