I don't know much about package managers, but instead of demanding every app uses the same version of every library, or including all libraries in every app, wouldn't it make more sense to allow different versions of libraries to exist next to each other, and every app simply picks the more up to date version that it supports?

I think that's how npm does it. Not that npm doesn't have its own dependency hell, but that's because different dependencies within the same application can end up requiring different versions of the same sub-dependency. But that's a problem only for developers.