Server side sessions aren't the bizarre practice - Keeping track of navigation state on the server side is.

This is like your whole website existing as a single endpoint and making POSTs to the same URL to get to different parts of the site.

...which is pretty much how hashtag-based single page webapps operate.

Many, if not most, isomorphic react/node.js apps have a single API url, with microservices behind the load-balanced URI, that accepts HTTP POST requests, and looks at a JSON object sent as the request body, in turn responding with a JSON object that informs the client-side app to re-render accordingly.

This isn't bizarre at all. It is very, very common; if not the norm.