1. It is different from a package manager because it isn’t platform specific because you can add scripts for any distro or architecture.
2. It isn’t really comparable to something like that because it just stores and runs bash scripts to install stuff.
3. It can install any app, from anywhere, not just specific to zsh.
4. It’s mostly convenience. Also, not all websites have a script to remove once installed, or automated ways to update.

I don’t think any privacy focused person should use a proprietary operating system. This is another example.