The core problem of web UIs has always been managing state. People like statically-rendered pages because most state gets kept in a) the URL, and b) transient HTML elements, and both are highly visible and easy to deal with in robust ways. When you're forced to have server-side state it's exceptionally painful, but people usually just avoid it altogether which in most cases pushes things towards the virtue of having less state anyway.
For complex UIs with lots of little interactions the above story doesn't really work, so we've invented state management systems for the client. Managing complex state still sucks, but it sucks less with these tools.
Sounds like this approach is just moving that state store back to the server, with a greased pipeline so it isn't so horribly painful to add new pieces of state even though both sides are involved. But you'll still face all the same problems you face with a front-end store: transientness, cache-clearing, even modeling is hard when you're dealing with a big blob of mutable state. And there will be the additional challenge of associating this stuff with a user (which you get for free on the front-end, even with modern state stores).
> Let the browser maintain a DOM tree that templates over a JSON object, then reactive-ly update and it's an amazing experience. You have minimal data transfer, and minimal rendering updates. There is a great deal of power in having your UI be a stateless function over a giant JSON object.
> this is where I have my shitty idea of a programming language for board games
It's funny, I started building a web-based board game to play with family during quarantine, and I landed on this exact approach totally by coincidence :) I'm using polling requests instead of websockets because I'm lazy/it doesn't need to scale, but it's the exact same idea where the server just publishes a giant JSON object of state and the clients are pure functions of it (and send messages to the server to mutate it). I wonder if there's some aspect of board games that pushes one towards that line of thinking.