I don't think you should be allowed to kill in self-defence. This is how it works in my country:
In my country, defending yourself is not considered an inalienable right. Right wing and left wing agree that the democratic government should hold a monopoly on violence. If you shoot a burglar to death, you will be convicted of murder or manslaughter (this reduces the incentive to use violence for the burglar). In any threatening situation you would never be allowed to use more force than the minimum needed to defuse the situation, which depends on the following factors: 1. The threat level of the assailant. If the assailant has no weapons (not even a blunt instrument) and you are significantly stronger than them, you would be expected not to use any kind of weapon yourself (the minimum amount of force to defuse the situation would be to restrain the assailant or scare them away). Notice how this incentivizes criminals to not use weapons. 2. Who is under attack. If you are alone and faster than the assailant, you can just run away. If family members are sleeping close-by, then more force would be allowed. 3. Other circumstances. This is a bit vague, but it can include stuff like whether there are other people around who you can run to, or your mental state during the attack.
In this case, they should have just noted down the register plate number of the robber and called the police. That would be enough to catch the robber later. Security camera footage would be enough to convict him. Any loss by the business, assuming the robber did not get caught, would be covered by insurance. What happened here led to an avoidable death, and put innocent by-standers at risk.
