If you say: If you regard the husband’s right as the effective cause, then why is there no waiting period for a woman divorced before consummation?

The answer is twofold:

First, we say that the effective cause is neither merely the husband’s right nor merely establishing that the womb is free. Hence, the reason for the obligation of the waiting period cannot be restricted solely to the husband’s right or solely to establishing that the womb is free; rather, there are multiple underlying wisdoms.

Second, we say that when a man has not consummated the marriage with her, his heart is not greatly attached to her; this is why he divorced her before consummation, unlike the case when he has consummated the marriage with her.