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if punishment doesn't work, we can stop wasting time on it and expend our energy on more constructive responses to undesirable behaviour

I think this is the crux of my disagreement.

I don't see how the validity of determinism has any bearing on the efficacy of punishment. Determined or not, people react to punishment in measurable and generally predictable ways, if we discover that all human actions are determined, nothing has changed, all the same motivations for punishment remain in place; it (ostensibly) continues to discourage undesirable behavior, communicates society's disapproval of that behavior, and provides victims with a sense of justice. If anything, determinism only underscores the notion that individuals will react to stimuli, a fact that is equally true if those reactions were "freely" chosen by the individual.