The stability of society and the law based facilitation of peace are absolutely within the mission of police forces and highly facilitative to the prosperity of a society.
I was once involved with a project that returned determination of land ownership from people's physical custody to the courts and the resulting drops in assault and homicide rates (for the entire country) was in the double digits over a period of months.
> Sometimes even a minute or two is the difference between you being alive or dead.
This is especially true when you are likely to have guns in the home. I'm countries with virtually no private ownership of guns, it is extraordinarily unlikely to be in life threatening danger in your home.
People who rob you with baseball bats and axes, and don't even think about the possibility that you'll have a gun, don't feel the need to kill you at any suspicious twitch. The axes and knives and baseball bats are there to have clear superiority, and they know you can't really harm them. So, unless you actually try to fight, you're quite safe from a physical perspective.
Conversely, if people with guns think there's a decent chance you have a gun too, they'll be terrified of any move you make and have a high chance of misinterpreting any gesture you make into violence. So there is much higher tension.
Of course, there is a possibility that you're being attacked by a crazed murderer - in which case you're probably going to die either way. But this happens vastly, vastly less often that robbery.
You can take a look at crime stats from even the poorest European countries. The proof that lack of gun ownership in no way causes more violent crime is evident. Everything I just added above is an explanation of why this happens, but the fact it happens is not up for debate.
You're naive. The police (or whatever you call it) is meant for inward force projection of the state. Your security is not the main concern.
Besides the police works too slowly to truly protect you when SHTF. Sometimes even a minute or two is the difference between you being alive or dead.