Obviously most distributions provide package managers that should be used for unified automated update mechanisms and gpg signing. Superior to curl | sh in every way.
The response of "it depends, we probably used your system package manager" was not often well received. Users who know how to use their package manager tended to just do that anyway, and not use the script.
In all cases, signatures and repositories need to be configured, often requiring both root access and usage of the CLI and in all cases much harder than running an installer script (which might be doing exactly these steps).
To achieve easy means of installing using distro package managers means including the application in the distro itself, but now it's beholden to the distro's software update policies and thus stuck on that specific version for years or even decades.
That is not what a v0.something of an end-user centric desktop application wants for themselves.