Inspired by a similar docker answer with a slight modification, adding the a
was the missing magic in my case:
WARNING: This will delete every image! Please, check and double check that it is indeed what you need.
$ podman rmi $(podman images -qa) -f
Again, please use with caution and make sure you know what you're doing! Sharing here for my own future reference and hoping that it will save someone else some time.
Thanks to the hint by @Giuseppe Scrivano there's an alternative which may be more natural (previous warning applies):
podman system prune --all --force && podman rmi --all
See podman system prune --help
for details. I have not yet had a chance to verify that this second method fixes the "image has dependent child images" error.