How to install and enable a default and admin theme in a Drupal 8 install profile with just YML (without using hook_install() or a .profile file)?
Ah ‍♂️. Trying to install my rutherford theme via the web UI gave a The rutherford theme was not found. error message, so it seemed the theme was at fault, not the profile.

I inspected my theme's info file and realised it had a dependency which was not being met. Commenting out the dependency got everything working again!

It's a shame that the php www/core/scripts/drupal quick-start rocket did not give me any errors about this unmet theme dependency, otherwise I would have saved about six hours of trying various different configuration approaches! Ah well, ce la Drupal!