I am really demoralized that vets -- who supposedly love animals -- would go for something that shoddy. A used car salesman, maybe. But a vet?
I've had similar situations myself, especially where I was heartbroken over a sick or dying pet, and the vet kept doing procedures without telling us it was A. hopeless and maybe even causing the pet suffering and B. it was going to cost a fortune (no actual prices named nor choices given).
It is especially sad with tiny birds like parakeets; there is not a lot you can treat them with when they get sick. I had a sick keet (many years ago) and the vet (not even an avian specialist) took the bird, and intubated him -- very likely killing him in the process. Then they did not call me for almost 12 hours; when I called after work to see how my bird was, the receptionist said "oh yeah....it died right away" (!!!!). Nobody bothered to tell me. The vet blamed it on the CAGE -- a fancy bamboo cage -- he said it wasn't suitable. And they would not return the cage until I paid the bill!
Just very sorry for your experience.