Re: If they'd done it 'properly'
If Microsoft had set the default option to 'private' then they'd have been inundated with help-desk calls from people who were trying to make documents public and failing because they hadn't read the details or been able to find the options menu item. This is how most people are, in the 'ordinary world'.
So your contention is that risking everyone's privacy is cheaper in support costs than doing it right. In the days before "we will fling everyone into a forum so users work for us instead of us having to offer support ourselves" that one could have flown, but not now.
Nowadays, that is be akin to disabling ABS by default because the clunky sounds of it engaging could scare the driver.
That said, you still could be right because if there is something that Microsoft has not been very good at it, it's creating simple user interfaces. Maybe they couldn't take the chance..