I think we're really in agreement about everything. The tools have intended jobs; some people use them incorrectly or without regard to best-practices. Both have different strengths and failure modes.
I would say JSX and the separation of presentation / behavior is orthogonal.
JSX is just a Javascript powered embedded SGML-like document.
The combining of presentation and behavior is caused by render() being defined inline with implementation.
You can not use JSX by using ReactDOM directly or a templating library while still keeping render() inlined.
Or you can move render() to another class (or subclassed, or HOC, whatever) and separate the presentation and behavior with or without JSX.
I like JSX quite a bit as well; IMO creating an artificial separation between presentation and behavior is not a useful way to think about web apps.
Separating data from presentation and behavior is fine, and is a long-standing GUI tradition.