Yes, if we can both pre-commit in a binding way, that's great. But what if we can't?

I feel that this is related to the intuitions on free will. When a stone is thrown your way, you can't change what you'll do, you'll either duck, or you won't. If you duck, it means that you are a stone-avoider, a system that has a property of avoiding stones, that processes data indicating the fact that a stone is flying your way, and transforms it into the actions of impact-avoiding.

The precommitment is only useful because [you+precommitment] is a system with a known characteristic of co-operator, that performs cooperation in return to the other co-operators. What you need in order to arrange mutual cooperation is to signal the other player that you are a co-operator, and to make sure that the other player is also a co-operator. Signaling the fact that you are a co-operator is easy if you attach a precommitment crutch to your natural decision-making algorithm.

Since co-operators win more than mutual defectors, being a co-operator is rational, and so it's often just said that if you and your opponent are rational, you'll cooperate.

There is a stigma of being just human, but I guess some kind of co-operator certification or a global meta-commitment of reflective consistency could be arranged to both signal that you are now a co-operator and enforce actually making co-operative decisions.