It's not an extreme solution. Regular policemen aren't armed in several countries: https://www.washingtonpost.com/news/worldviews/wp/2015/02/18....
Nothing's going to happen to you walking around the south side of Chicago unarmed. It's this kind of cowardice and paranoia that causes so many police shootings in the U.S.
And those countries that article lists are the definition of apples to oranges when compared to the United States. The economic, cultural, gun ownership rate and racial situations are completely, utterly different. To use the logic that something works in any of those countries, particularly Iceland, therefore it'll work in the United states if just blindly applied, is the height of ignorance.
People of a particular political persuasion who do not live in Chicago (and, probably, many people of that persuasion who do) like to believe that violence in Chicago is motivated by race or class. In fact, white dudes carrying laptop bags are not the natural adversaries of the people doing the shooting in Chicago.
I think you should stop talking about Chicago now; the examples you've provided, all of them poor, are not making your arguments more persuasive.
What I won't let you do is move the goalposts. You invoked "south Chicago" as a symbol of urban violence so great that a person like yourself couldn't function in it unarmed. That was bogus on several different levels, only a few of which we've described so far.
Norway has 31.3 guns per capita. Iceland has 30.3. The US has 112.6.