The majority of my birds have been rehomes. In fact, out of my flock of 7, only one is not a rehome - which isn't even counting the foster bird!
My first conure was a rehome, and we never did have a strong bond that you see with most tame and friendly birds. Truth is, he really wasn't friendly. Sure, he'd step up and he learned to enjoy kisses, but given the choice, he'd prefer to be in his area or out on the apple tree. I still think that we had a special understanding of each other. He had at least two homes prior to mine and I doubt he was understood in the last home. In his first home he was attacked by a ferret, which is what resulted in him finding a new home. His owners couldn't afford the vet bills to get him right again and the vet didn't want to put him down.
My second conure, Charlie, "kind of" bonded to me instantly. He lived with 1 man for about 10 years of his life (so was supposedly a "mans bird"), lived in a pet store for about a year, then in foster for another year. While at the pet store he did bond with a young girl, and while in foster he did bond with the couple who cared for him (the man more so than the women). I went down there and stayed at their house for a few days and he wanted nothing to do with me! Why should he? I'm a stranger! Once I brought him home, I went from "stranger" to "safety" - I was the only familiar thing to him in an entirely new environment. He's now bonded to me.
Jayde, my third conure, did take some work! I think she was with her first owner for 1-2 years, then she went back to her breeders home, then to foster care for 6 months and then to me. I don't know how she was in her first home, but I know that she couldn't be handled while in foster care. She *loved* being baby talked to and *loved* getting scritches, but she would not step up. I honestly don't know how she didn't warm up to her foster mom, considering she warmed up to me rather quickly! She was very nervous and skittish at first and required the safety of her cage in the first few months of having her, but now that she has settled in, I can't keep her off me! LOL
With the ARN that I'm fostering, I'm guessing it's going to be a while. I don't think she was ever a pet, merely a "pretty bird" sitting in a cage. I don't have any history on her unless she is the bird I think she might be, then I have limited history on her! She could very well be in her teens or twenties and I need to somehow make her into a pet... at least, far enough that she can be handled and interacted with, not necessarily a lovey dovey bird. If I can help her to become a "pet bird", then I can help find her a home where she'd be happy in.
I've also had quite a lot of rehomed tiels and parakeets (not just budgies!) and depending on the birds and how I felt at the time I either tamed them (at least as far as getting them able to step up) or allowed them to be content without taming them. I don't feel as if every bird needs to be tame in order to be happy, so I'm perfectly fine if the majority of my birds aren't tame as long as they are happy! And if they show interest in wanting human interaction, I'll provide it! (which actually happened with a previously tame tiel, and because she did it, another tiel wanted the same, and soon I was hand feeding all my tiels, tame or not!)
I've had birds for going on 14 years and I have yet to have a bird choose me. The majority of my rehomes are actually from people who knew I had birds, loved birds and wanted to know if I wanted another bird! Jayde I actually picked.
The person that I got the ARN from actually wants me to keep the bird, but I don't feel as if I need any more birds! And I met a mechanic that I have "wowed" about my knowledge of birds (as compared to his knowledge - which is lacking - and Chuckie, his conure that only eats seeds and whatever poor choice of foods he feeds them readily ate the pellets I provided for him!) and he wanted me to take his two birds home for a day or two to get them eating healthier! (instead, I brought some of my own food to him, so he has an idea of what I feed! and now he's willing to pay me for buying food for his birds, or making up a batch of my mash food!). The guy seems really thankful that I'm willing to help him out in caring for his birds, and he realizes that his conure does need some help! Since Chuckie barbers his feathers....
(supposed to be taking in a cockatoo later this year, but it doesn't look like that's going to happen, atm)
So I'd really say it depends on the birds, depends on the kind of situation they are coming from, and the kind of relationship you want with the bird.
