However, I wonder why this additional option, as depicted in this image
is not generally available when editing the folder format directly from preferences->folder format.
First I do not see this option at all when modifying my already customized favorite format
That checkbox being disabled in Preferences for collections is a UI bug/oversight. We'll get that fixed.
(Favorite formats don't have the checkbox as it doesn't apply to them; it's only for formats that other things can inherit from.)
You can turn it on in another way, by going to the collection, then opening Folder > Folder Options, clicking Save and selecting the option to save for sub-folders.
(Another alternative that should work is a wildcard path format, but that's more work to set up.)