I imagine by the time you see the tiny drone and are able to aim at it, it's likely too late. And what if it's a kamikaze drone and the explosion is bigger than anticipated?

Telling your soldiers to shoot at that sounds riskier than "take cover as soon as you think there's a drone".

Anyway my understanding is that so far drones are more useful for destroying stuff than killing people.

A much simpler countermeasure to armed drones is a net.

As for surveillance drones... I'm not sure militarily speaking they care all that much. The enemy already could be watching them with satellites, high altitude drones or balloons that would be nearly impossible to detect, or plain old binoculars, anyway.

Unless it's a covert operation, in which case the enemy launching a drone to find you is already very bad.