But this seems to have more to do with fairness than with commitment.

Fairness? More like easy, common sense. You play tit for tat, opponent defects, you defect. If opponent keeps on defecting, you defect too. Simple winning strategy for you, to which you should absolutely precommit to.

Your opponent, knowing your precommitment, can't really do much. Strategically speaking, he's the one to act, as your precommitment to tit-for-tat works kinda like removing your steering wheel in a game of chicken, making you indifferent and unable to stop. He can crash you just as many times as he wants to, but the choice is always left to him.

And why it is his? Because you're precommitted to a strategy, but he, by defecting, he either strayed from his precommitted one, or revealed that he didn't have any to begin with. Now that he doesn't play pure tit-for-tat, his second best choice would be co-operating twice and continuing with tit-for-tat. To him, strategy "play tit-for-tat, defect once, continue with tit-for-tat" is quite far from optimal.