Checkbox on page options are confusing

I'm finding the checkboxes on page options quite confusing, and suspect they could be improved. THey make sense once you figure them out, but for a first time user (or a non-technical user) I think they will continue to be confusing. For example, here is my experience setting up my very first test page. I create the page, write some stuff, and go to options to ensure it's not published before I save the content. We are greeted with this UI:

If I click "No" then it enables the frontmatter key for published, and sets the value to false e.g.

Ok, that's a little non-standard for a checkbox.....I'm confused why the checkbox was selected when I just clicked "No". I think this is probably a common confusion - it's unusual for a checkbox and a toggle button to have to be used in tandem. In my confusion, I uncheck the checkbox. "No mr. silly admin plugin, I really do not want this page published please stop trying to select published". I now get this UI:

At this point I'm feeling good - I fought the confusing JS and won the battle. Then I click save....and it toggles back to 'Yes'...

At this point I just went to a different screen (Manage Pages) where the published vs unpublished status is displayed clearly.

-- End of Story

This happens for other plugins that use the options - MathJax has a similarly confusing setting, and IIRC it will by default will serve the mathjaax css/js on every single page unless you go into the options, click the checkbox to enable the mathjax setting, and then click the no toggle.

Short-term, it would be good if there was some minor JS added to ensure the toggle slides back to "Yes" if you uncheck the checkbox - that would be good instant feedback rather than the unpleasant surprise of seeing it change when the page is saved.

Long-term, perhaps some help text icon saying "default state is enabled" or something? Or a cleaner UI in some other way - I get that we are trying to display the difference between a notset-yes-no, but perhaps just a 3-way toggle between those options would be a better choice?