The old way was to return HTML fragments and add them to the DOM. There was still a separation of concern as the presentation layer on the server didn't care about the interface presented on the client. It was just data generally composed by a template library. The advent of SPA makes it so that we can reunite the presentation layer (with the template library) on the frontend and just send the data to be composed down with the request's response.
The issue with this approach is to again split the frontend, but now you have two template libraries to take care of (in this case one, but on the two sides). The main advantages of having a boundary is that you can have the best representation of data for each side's logic, converting only when needs. And the conversion layer needs to be simple enough to not introduce complexity of its own. JSON is fine as it's easy to audit a parser and HTML is fine, because it's mostly used as is on the other layer. We also have binary representation, but they also have strong arguments for their use.
With JSX on the server side, it's abstraction when there's no need to be. And in the wrong place to boot.