When a criminal chooses to use a lethal weapon such as a gun, they do so knowing that they may end up killing someone. They also know that by using that weapon, other people may use lethal force in return to defend themselves, or law enforcement may respond with lethal force on behalf of the general population. The criminal chooses to uses a lethal weapon knowing they may kill, or be killed.
Likewise, law enforcement officers know that at some point in their career they may be required to face an assailant with a lethal weapon, at great risk to their own life, and they may have to use lethal force against such an assailant to protect themselves and the general public. When they chose to become a law enforcement officer they did so knowing they may have to kill, or be killed, as part of their duty.
Is the general public willing to make these choices? To kill or be killed? Is your mother willing to carry a lethal weapon, knowing that at some point in time she may have to kill someone, and risk being killed herself? Your grandparents? Your spouse? What about your children? At what age do you let a child carry a lethal weapon to defend themselves from armed bullies?
If arming everybody makes society safer, then why not just give every single citizen a government issued gun when they reach a certain age and be done with it? Seems fair. A few 'bad' people would get guns, but more 'good' people would too, so it's a net win right? And if someone chooses not to carry their government issued weapon and happens to be killed by a 'bad' person, then you can just blame the victim. It was their own fault for not carrying their weapon.
What if the 'bad' guys start carrying bigger fully automatic machine guns? As you say, these people don't care about laws or restrictions. Do we then let everyone carry bigger weapons? What if the 'bad' guys then start wearing bullet proof vests? At what point does the escalation stop? Do we then create some magical law that not even the 'bad' guys will escalate past so that all the forces balances out nicely?
I don't think reality is as simple as arming more people.