The problem with a central script repository is that bash scripts are difficult to audit, both for malicious activity, but also for bad practices and user errors.
A steam bug in their bash script once deleted a user's home repository.
Even though the AUR is "basically" bash scripts, it's acceptable because they use their own format that calls other scripts other the hood, and the standardized format makes it easier to audit. Although I have heard a few stories of issues with this, like one poorly made AUR package moving someone's /bin to /opt and breaking everything.
So in my opinion, a package manager based on bash basically doesn't work because of these issues. All modern packaging uses some kind of actual standardized format, to make it easier to audit and develop, and to either mitigate package maintainer/creator error, or to prevent it entirely.
If you want to install tools on another distro that doesn't package them currently, I think nix, Junest, or distrobox are good solutions, because they essentially give you access to the package managers of other distros. Nix in particular has the most packages out of any distro, even more than the AUR and arch repos combined.
Just because I trust the authors to write good software in a popular programming language, doesn't mean I trust them to write shell scripts in a language known for footguns.