When I use static sites for projects, one of the reasons that I'm doing it is to keep costs down. If I really wanted to have a comment system on a static website, I think what I'd create is a system in which I have a server for the first visitor, but then for every other concurrent visitor, I'd use a P2P WebRTC connection to send the comments over. Signalling servers are free, if you know where to find them. And I can use my own server as a TURN server if needed.

So the model really is: offload whatever you can to the user. Or just don't have comments :)

If the website wasn't static, then I'd simply just use a server.