Two things are usually claimed for recapitulation by those who prefer it, and one thing is usually held against it.
The first claim is that it keeps the incarnation and the cross in a single continuous act. On the transactional accounts, the incarnation is a precondition: God has to become a man in order for there to be a man who can pay, and the payment is the point. On recapitulation the whole life is the work, from the conception to the resurrection, and the crucifixion is where the work meets its hardest resistance rather than where a separate transaction is executed. Those who value this argue that it explains why the Gospels spend so much of their length on a ministry rather than moving directly to a passion narrative.
The second claim is that it does not make God a party in need of something. Nothing is owed to anyone in this account, no wrath is discharged, and no honour is restored, so the objections that press hardest on satisfaction and penal substitution have no purchase here.
The objection is the mirror of that second claim. If nothing is owed and nothing paid, a critic asks, why must the repair pass through an execution? Recapitulation gives a strong reason for the incarnation and a weaker one for Golgotha specifically. The usual reply is that death is the last stage of the human course and the one Adam could not reverse, so a course run to the end must run through it, and that the resurrection is what makes the reversal visible. Whether that reply is sufficient is a real question and not a rhetorical one.
Recapitulation is also the model most often paired with theosis in Eastern Orthodox theology, where the language of a nature healed and raised carries directly into the language of a nature made a partaker of the divine. The pairing is close but not identical, and reading either through the other flattens both.