The last (big) release of Publii, published 3 days ago, allowed me to try Cusdis.
Cusdis is an open-source, lightweight (~5kb gzipped), privacy-first alternative to Disqus. It's super easy to use and integrate with your existing website. We don't track you and your users.
It's still a service, with all the risks that this entails, but I think that, weighing all the pros and cons, it's still worth to try and use it, as it adds an interesting layer of interaction. And to be honest, managing comments without using external services is a pain. It would be hard enough on Joomla, simply impossible with Publii.
So it seems that we now have comments. Yay! \o/
UPDATE, April 19th: Cusdis website seems to be down. Not sure what is going on, disabling it for now.
UPDATE, April 20th: Cusdis has come back to life \o/