Your description of cut-through switching isn't quite correct.
If the packet is corrupted, there is no need for the switch to intentionally break the CRC, since the only way it knew the packet was corrupted in the first place was the broken CRC. Modifying the existing, broken CRC, would create a small chance of accidentally "fixing" the corrupted packet, whereas just continuing to forward it would ensure that a later (store-and-forward) switch, or the end-host would detect the broken CRC and discard the packet.
If the packet is corrupted, there is no need for the switch to intentionally break the CRC, since the only way it knew the packet was corrupted in the first place was the broken CRC. Modifying the existing, broken CRC, would create a small chance of accidentally "fixing" the corrupted packet, whereas just continuing to forward it would ensure that a later (store-and-forward) switch, or the end-host would detect the broken CRC and discard the packet.