Why should a developer of a free and open-source application, provided free of charge and without any guarantees, have any obligations to package and even test their software on random, thirdparty distributions?

If a distro wants to include their application they have every right in the world to do so. So its up to them to do what ever is necessary to enhance their product with the freely available product of the unpaid developer who created it.

History has shown that application developers are very bad at releasing good deliverable without too much security holes in the packaged libraries or bad practices. And the sandboxing in flatpak is actually meant to protect users from harm done by clueless devs but it fails because devs can actually build non sandboxed flatpaks and they will do it because they don't care

It’s called a distribution. Literally distributing the software. The distro deals with integrating all the packages into a single compatible system. This includes setting options to maintain system compatibility.

Packaging is not required for testing individual applications. That happens at build time and the developer writes the tests. These are not distribution specific.

The separation of concerns is very clear. If a distribution doesn’t package the code then the user is left to build the application themselves. It’s impractical that a developer would build and maintain their own packages for every flavor of every distribution.

No. I trust distribution maintainers a lot more than I trust other developers.

You can't have distro specific policies using this methodology.