I vote yea, so that the admins' lives are that much easier.
If we're really taking a tally, though, you might want to add a poll.
Edit: Also, if I can make a game private I'm inherently more comfortable posting material I publish personally under OGL parameters. If anyone can grab it automatically then it limits what I'll use of the material I would create and use on the site. I've used private games on another site back in the early days of 3.5 where I tested materials before publishing them and am looking at doing so currently. If there isn't an ability to privatize an entire game I will likely just not playtest said materials here at MW. As I respect the feedback of many individuals here at MW that I've played with over the years that in itself is a resource that is nice to have access to. Broadcasting fresh creative material to masses of individuals and watching that content spiral out of my control on the other hand isn't something that I would be all interested in.
Would there be a viable alternative perhaps in requesting private games instead of making the option freely selectable? Perhaps a combination of that or based on post count to allow more experienced users to still make them?