So it's possible to build a WordPress theme that uses it's own API for all the data, making an entirely client-rendered site.
I would have thought there would be a bunch of themes like this available, but it seems it's still new enough of a concept there isn't that many. That I found, anyway. I did find Foxhound though, by Kelly Dwan. It's simple and quite nice looking:
It's React-based, so the whole thing is logically busted up into components:
I popped it up onto a test site and it works pretty good! So that I could click around and do various stuff, I imported the "theme test unit" data, which is a nice and quick way of populating a fresh WordPress install with a bunch of typical stuff (posts, authors, comments, etc) for testing purposes.
About 50% of the URL's you click load instantly, like you'd expect in an SPA type of site. Looks like any of the links generated in that shell page that PHP renders do a refresh, and links that are rendered in React components load SPA style.
I would think this would be a really strong base to start with if you were interested in building a React-powered WordPress site. That's certainly a thing these days. I just happened to be looking at the Human Made site, and they say they did just that for ustwo:
ustwo wanted to build a decoupled website with a WordPress backend and a React frontend. Human Made joined the development team to build the WordPress component, including custom post types and a custom REST API to deliver structured data for frontend display.
So ya know, people are paying for this kind of work these days.