I have several tasks in my Org file, one of which has items starting with a checkbox (but only those).

I'm looking for a way to automatically update the parent task from TODO to DONE once all of the checkboxes are marked as done as well.

The documentation says:

If you would like a TODO entry to automatically change to DONE when all children are done, you can use the following setup [...]

Another possibility is the use of checkboxes to identify (a hierarchy of) a large number of subtasks (see Checkboxes).

The way I understand that last part is that if children items are checkboxes, parent state should already be automatically updated (which is not the case).

What am I missing?