You hit a chord here with me, I've moved away from WP to Hugo & Eleventy. For interactive features like comments, the search/sort/filter of databases is a strong draw though, and I'm already wanting to add search to Hugo. There's compromises in every approach, but SQL brings a lot to the table that flat files just can't do without a fair wedge of effort... or is there a tool/library that could index thousands of markdown files plus their comments in json/yaml/md format? Statically rendering the comments would give get me 80% of the way there, without free text search. Maybe I'm just ignorant of the tools available, blinded by my past experience and knowledge with older architectures.
I still wouldn't put them into Git along with the rest of the site, that's a definitely no-no. A separate Git? Also no for me. Filesystem does seem viable on reflection, and I feel inspired to explore this now.