Your idea has been tried several times, and was generally thought to work well for a while in each case. Thugs, terrorists and hooligans (and legitimate owners, but who cares about them) were stripped of their arms on several occasions throughout the past century. Germany leading up to Hitler, the former Soviet Union under Stalin, Pol Pot's Cambodia, and a host of other less publicized efforts were all in accord with your essential theory. Eventually each case led to lessons for the gullible public who allowed such notions to take hold.
Even here in North America, millions of people spent time in a similar gun-free utopia whenever they boarded a plane. They felt safe in their unarmed insecurity - they were passengers, not security guards. Money or jewels might need to be guarded with firearms because some baddies might want to take those valuables - but no one wanted to take their lives, and therefore (unlike their ancestors of every generation) they needed no firearms, they reasoned. The media had told them that they were 43 times more likely to die from a gun in the home than to shoot burglars - and who paid attention to the later corrections to that discredited study, or to the fact that in 98% of cases of defensive firearms use it was not necessary to fire even a single shot. Nobody cared - it was all academic research that didn't concern them because they didn't own firearms. Then thousands of them died in a single morning. It seems that some folks now prefer a new form of utopia in which citizens are possessed of the ability to defend themselves and their fellow man against bands of homicidal rogues who happen to be equipped with kitchen utensils, shaving implements, shoe bombs and the like. There are expensive ways to do this in specifically defined areas (eg air marshalls, national guard) and there are inexpensive ways to do this wherever there are people. CCW springs to mind.