CoinSwap doesn't require a third party, Bob can be alice and I noted this in the post. 
I just thought it was easier to describe using three (or four) parties then trying to make distinct one party operating in multiple roles... an effort to try to simplify some of that complexity you mention.
I just thought it was easier to describe using three (or four) parties then trying to make distinct one party operating in multiple roles... an effort to try to simplify some of that complexity you mention.Actually it would be simpler for me if they were only Alice and Bob.
I'm trying to compare it with the "classical" trading across chain contract but I'm not able to see what you gain with coinswap or having Carol in the middle.