I think when the warm moist air hits the cold dry air from the other rooms, you are beggin for a thunderstorm, or even worse, twisters. However small they may be.
Yes, I have an attic fan in my home. It is still not recommended to run an exhaust fan from a high humidity area (bathroom, kitchen, laundry room, fish room) into an attic. I wasn't picking on your recommendation but in my area of the country, it is not recommended. Building codes in my location prohibit this type of venting.
And you are absolutely correct. Moist air vented into the attic will condense and then drip back down into the insulation, and that is just the start of the issues.