Yes, it does have a package manager, but... , like you said, it's not as complete and it is different, which means you need to put in extra efforts to convert and make things work (also don't forget about a potential lib C compatibility fun). Why go through all this trouble though? Why not use the distro you are already using as-is and still get Alpine-like image sizes? One nice thing about Alpine is its hardened kernel, but you won't be using it in your Docker container. Alpine is nice, but it's not worth it when there are other alternatives that don't require extra time and effort I'd rather use to build a better product.

And if you are using 3rd party Docker images Alpine won't help :)

Has something like nix been considered for alpine? I think it would be really great for use in containers since it has the built in ability to garbage collect unused dependencies.