this is quite impossible. The simple fact is that you can not stop a crime until a law is broken. A cop could see someone in a ski mask with a crow bar walking down the street, and he can ask him questions. But unless a law has been broken a cop can do nothing.
Violent attacks in particular often last only a few minutes, sometimes the occur in seconds. Even if you have an emergency button that summoned the police to your exact location, they are still limited by the fact that we do not have star trek transporters, they have to move through traffic in a vehicle. Some areas of the US are so sparsely populated that increasing police presence ten fold would still mean that officers still might take a while to get there.
you also have the problem that officers often have very poor intelligence of what is going on when they arrive on scene. This can present many problems such as police officers waiting 40 minutes to enter a building in which a gunmen has been reported killing people because they need manpower to secure all the exits first. This could mean that cops arrive on scene and shoot a home owner six times after he has already detained the criminal and is on the phone with 911. The best person to have defend you is yourself because you have better situational awareness being at the scene of the incident first, so you are the best person to determine how to properly defend yourself.
As we said, cops are a deterrent and reactionary force. An assault/murder is usually over by the time their arrive on scene. Yes cops are needed to apprehend and the justice system is needed to prosecute, but neither of these things matter in the 30 seconds you have when someone pulls a knife on you. Even If you had a phone, you do not have time to call for help, you must react now.
Waiting for help to arrive is the absolute worst thing you can do in any survival situation. Having the tools to better help you survive is a very reasonable thing. A firearm being the best tool for my survival against an attacker means just that.
economically replacing firearms with police officers is impossible. Firearms are a positive force on the economy, while police officers are a drain on the economy paid through taxation. Just the yearly salary of one police officer can arm thousands of people. So no taking firearms out of the equation does not mean more funds for police officers because those funds used to buy firearms never belonged to the state in the first place.