Modern Wordpress hosts do both, and it's usually very very quick to load.
https://docs.joinmastodon.org/user/run-your-own/
Many people run theirs on a small VPS, raspberry pi, etc. and there are a number of 'paid hosting' providers for Mastodon servers too.
In practice, this all means yes: unlike a blog, it is a complex web application, and caching and whether a CDN is in use are up to the person hosting it.
Mastodon can also be fairly expensive to run, depending on how many images/videos people upload, traffic they bring to the instance, etc.
But basically, it's an essential part of a modern Wordpress stack (lol, what an oxymoron, I know), not an afterthought. It's not something a lone-wolf admin using a generic Varnish/Nginx config should do, but part of a large a community-driven effort to improve Wordpress performance. These plugins are very well integrated into the Wordpress base system and cache many parts of it.
This isn't so much to defend Wordpress (whose ancient architecture requires the use of these techniques), but to express surprise that a modern software like Mastodon doesn't have this built-in.
In hindsight, I should have used an indirect link via mastodon.social or something, apologies.