Of the three distros I know to more detailed extents, Debian, Arch and RedHat, none of those make it easy to install and keep updated a third-party package through the built-in package manager.
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.
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.