- Package managers allow you to avoid checking large (several megabyte or larger) binaries into source control. Doing so is anathema to many source control tools, the pervasive git being one of them. We had a repository hit Bit Bucket's size limits a couple months ago because developers were checking in CocoaPods. Another project was already halfway there when we migrated from SVN because we had been checking in all our lib binaries (and hadn't been using NuGet). Since package managers will download packages on the fly for each developer, they eliminate the need to check these binaries in.
- They prevent mixing incompatible files/libraries. Folders can contain mixed versions of the librarylibrary's files if someone doesn't clean it out properly during an upgrade. I've seen a case where half the binaries in the folder were upgraded, resulting in very weird bugs. (It didn't even crash!) It took us literally months (not man hours, just overall time) to figure out the problem. By letting the package manager control the entire folder, you can't get mixed versions; you ensure consistency. They also make it much harder to use incompatible dependencies, by automatically updating everything together, installing different versions where needed, or even just throwing warnings or errors when attempting to use incompatible versions of libraries.
- They establish a shared convention for managing libraries. When new developers come onto your project, team, company, etc., they're likely to know the conventions of the package manager. This means they don't have to waste time figuring out the fine details of how libraries are managed in your code base.
- They give you a standard way of versioning and distributing your own dependencies and files that don't belong in your repository. I have even personally leveraged them for some large static data files my application required, so it works well for versioning things besides binary code.
- Some package managers provide additional features during installation. NuGet will add dependencies and content files to your csproj file and can even add configuration elements to the config file.
- Their package list files document the versions of your libraries in a single, centralized place. I don't have to right click a DLL and look at the version number to figure out what version of the library I'm using. In Python, the library author may not have even included the version number in the py files, so I might not even be able to tell the library version from them.
- They discourage machine wide installation of dependencies. Package managers provide a conventional way of installing dependencies without a global installer. When your options are lib folder and global installation, many library developers will choose to offer their libraries primary as global installations rather than as downloadable binaries that you have to set up yourself. (MS history demonstrates this. It's also the case for many libraries in Linux.) This actually makes managing multiple projects more difficult, since you may have projects with conflicting versions and some developers will certainly choose the seemingly simpler global install over having their own lib dir.
- They tend to centralize hosting and distribution. You no longer have to depend on that random library's web site. If they go out of business, a successful package manager's site still has every version ever uploaded. Developers also don't have to hunt down many web sites just to download new libraries; they have a go-to place to look first and even browse for different options. It's also easier to mirror packages organized in a standard way than to manually host copies of everything from ad-hoc websites.