If there's no persisting consciousness or self beyond the aggregates, why is annihilationism considered a wrong view?

I have been closely following many of the answers on this forum in order to study Buddhist doctrines more carefully, and many answers such as this seem to state that the Buddha did not teach any transcendent consciousness, eternal self, or metaphysical subject existing beyond the five aggregates (skandhas/khandhas). Consciousness itself is treated as dependently arisen and included among the aggregates, rather than as an ultimate witness or substratum that survives them. However, if there truly is no consciousness, self, awareness whatsoever beyond the aggregates, then what exactly distinguishes the Buddhist position from annihilationism? If the aggregates cease completely at the Passing away of an arahant, in what sense is Buddhism not simply saying that the person is extinguished into nonexistence? Relatedly, why does Buddhism avoid saying that the liberated arahant is “annihilated” after passing if there is no continuing principle beyond the aggregates? In texts such as MN 72, the Buddha refuses to say that the Tathāgata exists after death, does not exist after death, both, or neither. But if there is no transcendent consciousness or self whatsoever, why is “does not exist after death” also rejected? More accurately if all possible designation is through the aggregates, and the aggregates cease, why is “he is annihilated after death” considered incorrect rather than simply accurate conventional language?