Since ANZ has decreased the cashback rate, I've decided to switch to SBS and AMEX free credit cards.
When I contacted ANZ customer service, they informed me that my cashback deposit date falls after the annual fee charging date. If I cancel my credit card before the annual fee is charged, I will lose the cashback I earned.
If I want to receive my cashback, I can't cancel the card until the cashback is paid out, which means I will have to pay the annual fee for the next cashback year. However, they also informed me that I can change my card to a Low Rate Visa, and the cashback can be paid to it.
Alternatively, I can request cancel the card after cashback is paid out, the annual fee will be refunded partially. However, they are not certain how the refund percentage will be calculated.