Why Carolina parakeets went extinct is very complex. I did a book review on a book that examined it, "The Carolina Parakeet: Glimpses of a vanished bird". It was very good. Multiple factors: egg collectors, nest & specimen collectors, agricultural pest, habitat segregation into little patches, them being poisonous to eat due to diet, communal roosting, nest hole competition, etc. The pet trade was actually not really a factor, which highlights fashionfobie's point about these issues being tied to other issues, both human & wild.
Apparently the budgie was declining in numbers in Australia in the late 1800s, so the government banned all export, & had the resources & inclination to enforce it. Budgies bounded back, but not every bird gets a second chance. Sun conures are gorgeous. I believe they & golden conures vie for prettiest conure. Unfortunately it hasn't done either any good. True confession: after my initial desire for an Amazon, at 7 years old, my more mature self zeroed in on those two. Thankfully, the internet existed by then & I could make an informed decision about not getting any of these. Part of why I chose budgies is because they've least concern status (not endangered).