In an edit media page, Ready for translation checkbox has no effect

When I edit a media using the list view (or if I click on "the edit more details" link using the grid view), I can see the "Ready for translation" checkbox. But even if I check it and save, it has no effect and the checkbox appear unchecked again.

Making this work would be a great way to introduce media translations.

Reproduce the issue from the WordPress media list view and the grid view's “edit more details” link, then trace how the “Ready for translation” checkbox is saved. Done means checking and saving the option leaves it checked when the media is edited again and makes the media ready for translation.

Written by the indexing model from the issue text.