Um, really? Eclectus parrots (and many other species) don't even reach sexual maturity until they're 2-3 years of age, so if they were dying within a year, they'd be extinct in the wild.
Actually that is very typical. I haven't been able to find much info on parrots specifically, but just to use a quick example I can think of - only 1/15 barn owls make it past their first year and they do not breed til they are 2 or 3. Those who do make it past the first few difficult years will usually live long enough to breed for a few years and can produce 2 clutches of babies a year if there is enough food. Remember, for a population to be stable, a pair only has to produce, on average, two babies that survive long enough to breed. Most wild parrots, except the largest species, will breed 2x a year or more. With the smaller parrots, a clutch may be 5 or 6 or more babies. Obviously the vast majority of those babies do not breed - or there would be a population explosion of parrots. Most die before breeding age or do not successfully find and defend a nest site That's another thing - competition for good nest hollows can be fierce and many wild parrots will also never experience raising chicks. Sometimes a pair will steal a nest site from another pair and kill that pair's chicks.
A wild parrot tends to live a short life that will end by being ripped apart and eaten alive by a hawk or other predator. Parrots that are sick, weak, injured, old, or just can't quite keep up with the flock for whatever reason are easy pickings for predators.
I think it is natural for us to want the best for our pets. It would be nice to have a huge fenced yard and a pond for my dog, but I do not. I don't think he misses such things that much. Along the same lines. I thought my birds would enjoy an aviary and built them one... big enough to enclose a small tree. But you know what? Even after spending many, many hours sitting in the aviary with them, they did not enjoy it or relax fully in it. That whole big sky to scan for predators always kept them a little on edge. I don't think they were unhappy outside, really, but they always seemed a bit relieved and ready for a nap when I brought them in.
I really think that parrots at good zoos or even good breeders that keep them in pairs or flocks in very large flights probably enjoy a better quality of life than most wild parrots. As for pets, well the way people care for their birds can just vary so much. Certainly there are many parrots who are neglected, fed poor diets, or kept in too-small cages, but there are also many happy, healthy, loved birds who live much longer and healthier lives than wild parrots.