Honestly, I'm not even sure what modern website are doing when they generate pages. I've had highly dynamic PHP/MySQL websites running on crap hardware, and it was trivial to attain .03 second page generation time. Didn't even need fancy caching, just some common-sense SQL optimizations.
At my last job we had an ad bidding API that would reach out to every advertiser we worked with, got the highest bid, then presented an advertisement to them.
The page was also framework after framework piled on top of each other, so they’d be using React and jQuery at the same time, stuff like that. And so marketing could change whatever they wanted whenever they wanted without breaking the entire site, everything was served from a CMS.
At a previous gig we had a similar situation. It was so bad my coworkers and I would joke that we needed one of those "break in case of emergency" boxes with the glass front and a hammer hanging adjacent. Inside the box: a can of lighter fluid and a match. The purpose: when the crazy got to be too much you just light own hair on fire and then go run around in traffic.
What you just described would definitely be a break the glass kinda situation :-)
Before going static as well I made a WP theme with Twig, removing most <?php wp_magic_function(); ?> from there. It was fast, way faster, than the usual WP themes. Obviously nowhere close to a static HTML.
Its not the HTML generation that's slow, it's everything that comes after. Usually lots of Javascript to run media and ads. Unfortunate, but it's driven by business decisions, not tech.
