Create a bootable installer for High Sierra under macOS Catalina
You are right - this seems to work only if the executing mac does support running the target OS. A download of 10.13.6 succeeds on MacMini7,1 and in a VM but fails on a MacMini8,1. Given that, it is likely you also get hardware specific builds if these are available for a given OS.

The installinstallmacos.py script lists all available options and does show Unsupported Board ID or Unsupported macOS version in cases that are not supported but it is able to download the installers from supposably the same source as the softwareupdate tool.

So either run softwareupdate --fetch-full-installer on compatible hardware, in a VM or use installinstallmacos.py.