I would say the same thing for baby bunnies. We have the same problem every year at the Humane Society. About a month after Easter we start getting people surrendering their unwanted rabbits. Many have to be euthanized because they are ill or injured due to improper keeping and care, and many were sick to begin with due to being purchased from bad "breeders."
It is so sad to see this. We do not accept birds at the AHS, but people still do leave their ducklings and chicks in boxes in the parking lot and they are almost always destroyed.
Pets never make a good gift and people should always make long term considerations and preparations before bringing any animal into their home. No animal should face euthanasia because it is unwanted.