But most of the European political elite want to unite the continent under a single government instead. Given that, the best kind of Brexit would be one where the UK is no longer a part of this, and can sign various unlinked bilateral treaties to continue cooperation in the areas where there is agreement, and discontinue in areas where there are disagreement.
This makes perfect sense - agreement on everything is rarely possible, so collaboration on the areas where people do agree is the best you can do. It's also exactly what the UK has proposed repeatedly. However the EU refuses to allow it, exactly because if people were offered that alternative the EU and associated gravy train would cease to exist tomorrow.
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.
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.