Well, I personally am in favour of the way the EU acts as a permanent umbrella to organise cooperation and according to the latest polls, the majority of people in most countries are in favour of that too. Otherwise, with each country acting on its own, they would be picked apart by the much larger players, the US, China and Russia.
Maybe the UK media points a wrong picture of the mood in the EU, but I seriously doubt that it would cease to exist if your alternative would be put forward. But that's something all Brexiteers tell themselves repeatedly, over and over, like a mantra.
I'm sure it would cease to exist. The EU has lost every referendum on further integration held in, what, the last 15 years? The EU political elites are notorious for telling countries that voted wrong to vote again, or just ignoring them.
If every population that's asked rejects the EU's vision what on earth makes you so sure that a comprehensive alternative wouldn't be popular?
Also there's no such thing as "picked apart" in the sense you mean, i.e. outside of military strategy. Nobody is picking North Korea apart despite that it's a world pariah. If a country doesn't want to collaborate with another country or accept its terms, it doesn't have to - the idea that cooperation is a form of warfare is exactly the mentality that the EU has, and is why it's so desperately dangerous and problematic as an organisation.
Maybe the UK media points a wrong picture of the mood in the EU, but I seriously doubt that it would cease to exist if your alternative would be put forward. But that's something all Brexiteers tell themselves repeatedly, over and over, like a mantra.