I can't speak for how anyone else uses React, but I'll use both functional and class syntax for different types of components as needed... I also break up my redux reducers against specific feature areas. I tend to favor redux/global state for many things, but will break out of this where it makes sense.
In the end, I find being able to reason about what a component is doing makes it easier to write and maintain them. I also absolutely separate areas of my applications by feature area. This may contain api/state/component combinations in whole or part.
I think my biggest issues regarding WebComponents, is they're difficult to write unit tests against. Beyond this, you cannot within the DOM pass state object and/or event handlers to child objects in a declarative way. This means you can't really write applications as easily (in my opinion). The way React works is much closer to how I conceptualize components than what WebComponents offers.
As an aside, JSX is absolutely something I enjoy that some disagree with. To me, it just makes sense, and it's so close to what I wanted when E4X was a good option with Mozilla browsers, Flash/Flex and VB.Net. Unfortunately lack of cross-browser support pretty much killed it. imho, JSX is actually better.
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