There are currently 23 nations that are without a military, and OH HEY LOOK, they're doing JUST FINE. They may allow for the Airspace protection by larger countries, but that just goes to show how much we should just make it illegal for a country to have a military.
Instead of a military, there should be the installation of small, defense-only militias or para-militaries, both of which are only active when needed.
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It's a nice idea, but the simple fact is that people are bastards. Nationalist pride isn't going away anytime soon, Militias would grow in size until they can take over the next country and so on and so forth. The other issue is, who would prevent other countries from growing too powerful or stepping on the path to conquest/invasion? You'd need something more powerful than them, to keep things in order. Things aren't that bad on the world stage at the moment though, sure the Middle east is an utter cluster-blam!- and there are one or two other countries at war with each other, but there aren't any major world powers kicking seven shades of shit out of each other anymore. MAD is what's kept the peace for the last 70 years, even if countries like the USA and NATO/UN are doing their interventions in the middle east and Russia is basically trying to rebuild the USSR. There is always going to be war, strife and conflict. The closest we will get to world peace is what we have now, when the middle east settles down that is <.<