Anyone who thinks they aren't broken should be made to don plate armor, carry bows and weapons, and a 45-pount hunk of plywood around. I don't think they would have the same opinion afterward...
Since you brought up real life I figured I'd chime in again. =o)
Actually plate armor isn't as heavy as the PHB says it is. Tower shields aren't as heavy as the PHB says their are. Are they heavy, yes. But plate doesn't weigh 50lbs and neither does a tower shield. Besides, with the even distribution of plate you aren't feeling any more then 7lbs of it on each limb and such. It's like carrying a 50lb backpack, except easier since all the weight isn't on your back.
Also most people that did wear plate and carry tower shields were of average strength. They didn't have no 14+ strength scores. Some might have but nowhere near a few.
I also think that most people when they think of tower shields think of mantlets, the things on wheels that were used to protect riflemen from musket fire.