Emotional commitment arises because the 100% foolproof (but, unfortunately, difficult) way to win a Prisoner's Dilemma is to credibly pre-commit to a strategy. Anne's (why not Alice's?) emotional reasons to play TFT are in effect a way to pre-commit to playing TFT; the most Bob can do is defect on the last turn.

If, on the other hand, Anne simply plays TFT because she thinks it's the smart thing to do, then the defect-on-the-last-X-turns strategy can escalate and result in everyone defecting. For that matter, Bob could try something like "If you cooperate when I defect, I'll sometimes cooperate... maybe" and test Anne's stubbornness.