I'd like to ask you a few questions OP.
Do you or do you not know the type of weapon most commonly used in criminal activity? It's a handgun. Handguns have basically no legal uses outside sporting, which we can easily sacrifice on the altar of getting a 80%+ involvement weapon off the streets.
We do this by simply preventing all sale of handguns. Sure, there are plenty out there, but then we prevent sale of handgun ammunition.
What have we just done?
We've made it multiple orders of magnitude harder to commit the crimes. Lets look at NYC and Chicago. Both have fairly similar gun laws, that is to say, lax by most first world country levels, but pretty intense compared to the reset of the USA. Why does chicago have such a terrible gun crime rate? Because there are places 15 minutes drive away that avoid the laws on sale etc.
So, it's clear from this irl example in the usa that restriction of weapon access lowers gun crime if done in a sane and sensible manner.
Total effect? A 80%+ reduction in gun crime as handguns become near impossible to source or source ammo for.
Of course, criminals will change to other weapons. Shotguns and Rifles, but these are much harder to conceal, have more expensive ammo, and cost more in general.
How do other countries handle this? They require the weapons be unsuited to applications other than sport / target / hunting shooting. Not only do you have to go through a large, involved and rigourous process to get a lisence for a rifle in NZ, it has to lack certain features of a military style semi auto.
So, lets look at the standard rampage killer in NZ. There isn't one. There hasn't been one for 20 years. Lets look at the standard rampage killer in Australia. There isn't one. There hasn't been one for twenty years.
Lets look at the guns / 100 stat? 30. Thats 1 gun per 3 people, which is fairly high among developed countries, but there are very few shootings of any kind and no shooting sprees.
This is all accomplished by requiring people to have have good reasons for owning a weapon (self defence if given as a reason is an automatic denial), requiring the weapons to be suited only to legal uses, a ban on handguns, and requiring weapons be stored safely and securely to prevent theft.
All of this comes together to give a population of firearm users who are simply not involved in crime statistics to any degree. NZ has 4 million people. We had 6 firearm homicides last year. That would correlate to less than 1 firearm homicide a month for NYC.
It's very easy to put enough problems in between a potential criminal and the crime that it's not worth it.