If you were to go the CSS/JS route for a theme modification, it is possible to have separate themes for separate sub-accounts. So you could add the necessary CSS/JS to only the sub-accounts that you want the modification applied to.
Alternatively, if you apply the modification at the root account level, you could add in an additional check about the course to see if the button should be hidden or not. I'm not sure how your courses are set-up, but if your blueprint and associated courses have SIS IDs while manually created courses don't, you could check if the course has an SIS ID before applying the change to hide the option.
Keep in mind that theme modifications like this don't fully prevent the ability to make the change since this doesn't modify user permissions, but rather it makes it harder to change since it hides/removes the option from the UI.
Also, that is a great Idea to check if someone has already submitted this as a feature request and if not, please be sure to submit it as a new Idea. I agree that this feature could be useful to help ensure a consistent online learning experience.