If one click on a tab-title of the editor, the content-area of the tab has focus. And that's great. As user I expect that sidebar and message window have exactly this same functioning.
[...] I agree that there don't seem to me much use for mouse-focusing the tab label itself for regular tab labels [...]
That is the point. There is no advantage, just confusion. If there would be much use for mouse-focusing the tab label itself for regular tab labels, then the editor would have the GTK default behavior, like the sidebar and the message window.