Its literally 20 times faster, and importantly, cuts across the human visual perception boundary, which is at ~200ms. So the old HTML version is human perceptible, while the new version renders in ~1 frame.
(Also, FWIW, loading delay of HTML pages on said beefy desktop, as tested right now, are consistently about 750-1500ms for me.)
More on-topic, these times apply only when the pages are hot in the browser cache. On my desktop, the first-time switch between "drafts", "sent" and "inbox" takes around 3 seconds each, and only then it is instantaneous. So regular users are likely to experience these long Ajax delays more often than not.
Even basic UIs like filtering can be bad if you want to change multiple filters, and you have to wait for a whole page load in between each change (page load times for pages with filters are often slow as they're performing complex queries).
It's a case of different things being appropriate for different use cases I think. There definitely are still times when plain HTML is best, but it's also not always faster.
I've built a React app that's under 300kb (cached with a service worker for subsequent page loads) that loads almost instantly and works offline. On the other hand, plenty of plain HTML sites include heavy CSS frameworks, or 5mb images, gifs, etc and load pretty slowly, especially on poor connections.