There's no need for two styles of package managers. GNU Guix and Nix can serve both purposes (and more) very well, for example.
I think language-specific package managers are fine for easily sharing source code amongst developers using the same language, but they shouldn't be used in a production system.
If you're on Windows, then fine use whatever is available. A language specific package manager is about as good as it gets there. There are no good package managers for Windows, and I don't think there can be. I don't even know if you can isolate builds in a container like you can on GNU/Linux. That's a crucial OS feature. Besides, I aim to liberate users, not enslave them, so I develop for the GNU system, not Windows.
The third sentence is not a contradiction. I'm just saying that I can live with people using language-specific package managers, but really they would be better off with a general-purpose one.
I think language-specific package managers are fine for easily sharing source code amongst developers using the same language, but they shouldn't be used in a production system.