I'm running wordpress on a weak shared server, so it has fallen over in the past.

I think if it was a static site generator (jekyll, hugo, 11ty) then there'd be no issue.

This is likely because the default MySQL connection limit is only 100 connections and your web server is trying to make more than 100 connections (MySQL is not available error). Then if you are using fpm, the default is just a small worker pool. A cheap server can likely handle thousands of requests, but all the defaults will limit you to under 100.