If the JSON protocol in question supports arbitrary behaviors and styles, then you still have an injection problem even over JSON. If it doesn't support them you don't need to support those in an HTML protocol either, and you can solve the injection problem the way we already do: sanitizing the HTML to remove all/some (depending on your specific requirements) script tags, event listeners, etc.
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If the JSON protocol in question supports arbitrary behaviors and styles, then you still have an injection problem even over JSON. If it doesn't support them you don't need to support those in an HTML protocol either, and you can solve the injection problem the way we already do: sanitizing the HTML to remove all/some (depending on your specific requirements) script tags, event listeners, etc.