Possibility of public humiliation is the main reason people watch sports according to Ann Coulter...
This! There is so much suspense and drama in a penalty shootout it's pretty much unrivaled by any other sport. Subconsciously the reason why people watch sports is the suspense. Appreciation of skill, tactics, physicality, etc. is secondary.
It's the same for my wife - she doesn't have the interest to watch a full game, but if she hears there are penalties she runs from the other end of the house, so she doesn't miss them. I imagine it similar for many people who watch football only during WC/EC - wonderful excitement and entertainment. Why would you want to remove this aspect of the game?
So what? It's because there is more pressure if you go second (assuming the first one scored). It's all about mental strength - it's not like the team that goes first gets an extra try or something. This is part of the game, the same with home advantage. Brazil is not the best team in this WC, but they are the favorite to win it because of home advantage. Is it fair? No. Would I propose to play the WC at a neutral ground in order to be fair? No way!
This is the only reasonable idea in the whole thread.