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.