but don't want to put any effort into finding a solution for said problem
Well, apart from campaigns of arson, terrorism and murder.
Your estimation is kinda incorrect anyway. For a start, most black metallers DO have a solution to the worlds problems (Normally to break the power of all judeo-christian religions). For a second, if you are a true misanthrope, you don't necessarily have any interest in improving the state of the world, which is, in your eyes, fundamentally fucked. This is why real black metallers spend most of their time in pursuits such as music, art, drinking, taking drugs, and running around in the woods covered in corpse-paint. Black metal is probably the only music genre to reach such heights of misanthropy that bands will vet who can buy their albums, or in extreme cases actually try and conceal the very fact they exist at all from the outside world, only giving tapes to those they can trust as being 'tr00' (though the cynical would say this is a marketing ploy, similiar to pressing only 666 copies of your debut album then instantly bootlegging it yourself. If it is, it certainly worked for Les Legiones Noires). For a third, remember the really important distinction between the three general sorts of black metallers:
1) true fucking black metallers. True fucking black metallers are 30 or maybe even 40 somethings who live mainly in Norway. They've been around probably since the beginning of the whole scene, and have been immersed in the whole thing so long they don't even have to try to be grim and krieg. It just comes naturally to them.
2) tr00 fucking black metallers. The fucking means a different things. These are teenagers who mainly live in the United States and desperately want to be 1. They have to try too fucking hard though. Any criticism of black metallers will almost certainly refer to this group, unless you're a huge fan of Norwegian stave churches.
3) people who like black metal. Don't really see what the fuss is about.