They have a product for that https://www.cloudflare.com/pg-lp/speed-up-wordpress-with-clo... It caches all pages on Cloudflare and only bypasses Cache on Cookies such as `wp-.|wordpress.|comment_.|wordpress_logged_.` which is used by /wp-admin/ are and when someone posts a comment. This turns your WP into static without doing anything special. Or you can write a custom cache rule for cookies using "Page Rules" or newly introduced "Cache Rules" beta https://developers.cloudflare.com/cache/about/cache-rules/
I used wp2static to archive a WordPress site recently, and I am disappointed with the performance.
The same website without Cloudflare CDN and just using a simple caching plugin is much faster than the exported version by wp2static hosted on Cloudflare pages.
It has fallen from 99 to 78 in the mobile page speed test.
I tried creating a copy of the website using wget, it was faster but i faced issues with missing files and posts on the main page using temporary query links and not the permanent links.
So I went through the Hassle of compiling wp2static and just eating the performance loss instead.
This would require you to host WordPress somewhere.
If you can host it on workers for example, you can get an entirety free, managed website just with one click(obviously someone would do a template to enable you to setup wp on cf pages if that was possible).
The same website without Cloudflare CDN and just using a simple caching plugin is much faster than the exported version by wp2static hosted on Cloudflare pages.
It has fallen from 99 to 78 in the mobile page speed test.
I tried creating a copy of the website using wget, it was faster but i faced issues with missing files and posts on the main page using temporary query links and not the permanent links.
So I went through the Hassle of compiling wp2static and just eating the performance loss instead.