Is it possible to make any changes to macOS through the Terminal or in another way, so that Launchpad allows simple uninstalling application files, downloaded not via the App Store?
It is possible but it's a bit "hacky".
Open your Applications Directory in Finder
Find an app the was installed from the Appstore.
Right click on the .app and select Show Package Contents.
- Now repeat the above steps or write a script to place that directory in all of the non Appstore apps by selecting Show Package Contents and pasting the copied directory.
Also I just tried doing this and it worked...
Looked up the app in Spotlight, held CMD to show to location of it, then went to the location,
(system drive) > users > (you) > applications
and for some reason was able to delete it from there (: