Many and varied are the ways to add comments to your static website. Most of them involve subscribing to services which, if you're running your own domain on your own server, might strike you as the wrong solution. "But," you might say, "if I want to have a comment system on my own site, it would not be static anymore. CGi's are so '90s and who needs the attack vector?"
In your searches, you may have come across Staticman which is open source and promises to be static... but the catch is that you need to be serving your site from GitHub. Even if you can put your domain name on it (haven't bothered checking), you are definitely not running on your own server and, at least for me, serving from GitHub misses the point.
Some of my sites have comments that were imported from Drupal. Obviously that mechanism is gone with the conversion to Jekyll, and even though I don't get many comments (that aren't spam) I still want the ability for my readers to comment. I just don't want spammers and hackers to have any weaknesses to attack.
To be honest, if no one had the ability to comment, I doubt anyone would care. I do have a contact form and my email address on all my pages if people want to connect. But, I developed a comment file system and wrote a generator to render my commented posts, so why not finish out a system that would work with a real, live interactive readership? My solution works for sites with small, calm readership because they need to email you, and wait for you read their email and then create a comment record by hand and add it to your site.
Having said that, I have no doubt that there are mechanisms that can be triggered by email to process a comment to add things to your site and cron jobs to process and push out your modified site, but that would be an exercise for the reader. ( ´ｖ｀)