Perhaps because Cocoapods is not an OS package manager or anything close to it. It installs libraries within the context of an XCode project, regardless of the host system or what is installed for other projects.
> The fundamental idea of downloading a list of available options of which the user picks some, and the system pulls in dependencies, is almost exactly how dpkg and yum work.
If you reduce it to the fundamentals you don't need yum or dpkg either to do that, just a dependency solver and curl.
I'd also consider removing a package to be a fundamental part of a manager. The two items you describe would be a 'package grabber'.