Why doesn't the military use these drones?

People here are obviously misunderstanding your question.

Understandably, when Predators and similar size drones crash, they're a potentially deadly collateral damage problem for civilians on the ground.

Your question basically comes down to several issues:

1. Weapons Delivery

2. Aerial Range and Linger Time

3. Fuel required for sustaining #2

While the military does use handheld drones (SEALs use the Raven, e..g.), they're short range. What you're failing to consider is the size of the delivery vehicle required for missiles. Granted, MAV's are primarily for unmanned recon; I still remember during the Gulf War when we were at the Pentagon we helped get the fledgling tech out in the field. But they're also quick-response/delivery units for onboard weapons, like the Hellfire missile, and you need a heavy / stable enough launching platform to shoot missiles from.

The other reason is aerial recon longevity. The reason that they have long wingspans is so they can remain aloft (linger) for many hours with minimal airspeed. Something like a quadrocopter (or regular fo that matter) wouldn't last, nor have the range of a Predator. Even if they were of a large enough size, their range would be limited to a point bordering on uselessness. If you're interested, the idea and technology for current drones (lingering flight capability) came about after Dick Rutan's Voyager plane circumnavigated the globe without refueling in 1986, one of the last truly exceptional flight records left to be broken.

Bottom line is that the use of a specific type of drone is based on mission type and range, not the possibility of collateral damage on the ground.

It's the missile that kills people not the drone... A Hellfire missile will work the same if it is fired from a MAV as it would from a Predator or Reaper drone...

Uh...why would that make any difference on killing people?

It is the Hellfire Missile that does the killing...not the drone

Might want to know a little bit about what you are talking about