Yes you can do that or there are static site generators backed by MySQL too. So your data and configuration site can still be dynamic but your served site will be completely static.

The only difference between this and adding a cache is that the cache is another piece of software in your production stack.

Can you recommend a good static site generator?

For WordPress? No. I don't use it. I just know SSGs for it exists and not enough people/companies use it (when they're using WP in the first place). :)

Vanilla SSGs are so simple I ended up writing a basic one out of a markdown and jinja parser in Python every time (for example: https://github.com/eatonphil/notes.eatonphil.com/blob/master...).

If I were not lazy I might learn one of the major ones like Hugo.

It doesn't matter what SSG you pick, they all produce the exact same kind of thing.

When my friends webserver died and they had no backups, I found the wayback machine was s good (historic) static site generator ;-) Just mirror it from there and voila.

Hexo is a good and fast lightweight generator.