Armed guards would increase the risk that someone is killed. According to German law, a guard would only be entitled to use its weapon in self defense, not in defense of the things to be guarded. Using a weapon is only justified when no other means is sufficient to ward off the threat to one's own or someone else's life. Shooting and killing a thief can result in a murder charge against the shooter. It would also make the job of the guards far more dangerous, when burglars are expecting armed guards and would be tempted to use violence first.
Not quite. Weapon use would be possible as "Rechtfertigender Notstand", https://dejure.org/gesetze/StGB/34.html . This doesn't just include protection of ones own life, but also of property. However, the force used has to be suitable and proportionate, so shooting someone dead would not be justified. Injuring someone would usually be justified, but will always land in front of a judge to apply 20/20 hindsight. And no one wants to accept that risk.
