I understand your concerns. However, my main concern is not merely liberating the birds from the cage. [Rinpoche knows they will be caught again] It is to be able to circumambulate with the birds around holy objects, to recite mantras and bless them in other ways so that they are given great benefits for the future, ultimate benefit. Here they make a connection to Dharma and can eventually be freed from samsara.
That is why I always give instructions on what to recite for animals and how to circumambulate holy objects and do different things for them, so they get the long-term benefit in the future of connecting with Dharma, good rebirths and enlightenment.
This is my long-term benefit for the animals that I buy.