I've never been involved with performing code reviews for Chrome or FF extensions but I'm not sure this type of attack would be detected by a reviewer.
Because if all they do is take the HTML response and send it over to some web back-end with an ajax request, that looks innocent enough to any reviewer. For example, under what grounds would a reviewer flag that ajax request as malicious and prevent the extension from being published? It's not possible for them to know what purpose that data has for the extension unless they are really doing a deep dive on each review and take the extension's purpose into account based on their opinion of what it "should" do based on its description.
I'd love to hear back from anyone who happens to review extensions for either browser.