You’re right that you don’t need a transaction to have precommitment (and precommitment may be good or bad, depending on the circumstances). But transactions make mutually beneficial precommitments more likely. Why should A precommit to stay with B? What’s in it for A? But if A precommits to stay with B in exchange for B precommitting to stay with A, now we’re cooking with gas.
You’re right that you don’t need a transaction to have precommitment (and precommitment may be good or bad, depending on the circumstances). But transactions make mutually beneficial precommitments more likely. Why should A precommit to stay with B? What’s in it for A? But if A precommits to stay with B in exchange for B precommitting to stay with A, now we’re cooking with gas.