Then a poorly written crawler shows up and requests 10,000s of pages that haven't been requested recently enough to be in your cache.
I had to add a Cloudflare Captcha to the /search/ page of my blog because of my faceted search engine - which produces may thousands of unique URLs when you consider tags and dates and pagination and sort-by settings.
And that's despite me serving ever page on my site through a 15 minute Cloudflare cache!
Static only works fine for sites that have a limited number of pages. It doesn't work for sites that truly take advantage of the dynamic nature of the web.