I really appreciate the way this thread has developed - I think it has done an excellent and relatively concise job of explaining why most kids shouldn't get a parrot, and why the ones who do should have parents who are as invested and well-educated as their child is. Sorry my responses are always so long...
As the parents are more likely (as likely as any adult, perhaps) to have a stable schedule and ability to commit time and funds, I do think that it is vital for them to be the default carers for any birds in family situations. Vet care is one that I can think of at least two cases on here where the parents did not understand or care about rapid vet responses and the birds paid for it. As home owners and their children's caretakers, they should also definitely be involved in risk management and enacting preventative measures (especially routines and behaviors) for the family to follow to decrease the danger of bites and property damage. Here is really where an engaged and educated parent shines, I think - it is a rare parent who will agree to putting ss corners on tempting doors or to not make that one sound that makes the bird do that hilarious temper tantrum just on the word of their child, but one who has hit the books and the forums? That seems like it would have much more of an effect.
One interesting possibility for family parrots would be having a juvenile bird grow up with the family, and the bird having the choice of who to stay with when the adult children disperse. This would potentially allow for a committed parent to also act as the bird's 'parent' diring its extended juvenile phase, and for it not to be uncomfortably trapped with its 'parents' once it reaches maturity. Of course, that is a very, very odd proposition for a family to commit to - "let's get a bird! Five to ten years down the line, one of you bird-crazy kids might just be picked, after we all deal with hormonal maturity! Otherwise, you can visit and might inherit the bird when we can no longer care for it!" Hmmm...
One problem with this idea is that it requires commitment in a time scale far, far beyond the actual behavior of most people (will my 11 year old, who loves the bird, actually be ok committing when they are 18?), and another is that it has the potential to be more of a commitment by the adult on the part of the kid that the kid will commit than a commitment by the kid, with full understanding of how their life may change in a decade as they fully assume the role which has never felt properly like their own before. Kids who wind up with birds as 'their bird' have much more of that feeling of commitment, even if they are fuly supported in their role, than kids who grow up with an idea of 'one day' committing.
But it might help all of the hand raised birds to feel a little less trapped when they want to have a special human all of their own, to have a family full of options when the time comes.
For birds with shorter juvenile periods, it would undoubtedly be better if they were brought home at a time when a child could fully commit... but it is still probably better for them to feel like they are involved in a flock/family than that they are stuck in the child's room with no other people who are willing to interact in ways the bird likes. Suk was undeniably enriched by her bonds with my sibling and parent, even if one of those (parent and default carer) was a hands off relationship and necessitated stick/cup training. Parrots are good at having rich hands-off relationships, and it is up to us handsy mammals to accept and enjoy those relationships for what they are.

Parrotsforlife and Pajarita (sorry I keep adding an extra 'r'!), kid flightiness is a good rule of thumb, but there are plenty of kids who can and do commit to many things. Musicians, athletes, artists, academics, and animal owners - all have many, many examples of people who started young and followed through with their commitment - their passion- for most or all of their lives. The difference with animals is that unlike the guitar, in weeding out the ones who are just trying from the ones who do, the animals have a high potential of being hurt. That is again why I think it is so vital for the family to be equally engaged and educated as the child, so that the commitment to try is spread across the whole household and doesn't overly penalise the child for changing as they grow up.
As for maturity, bonding and biting... I think that that needs to be both a parental decision (risk) and a family commitment to trying again and again in new ways; understanding that parrots like to have more than one type of relationship and that hands off ones are great too. Bird no longer cuddles? Let it cuddle who it likes, and when the disappointed one has processed it a little, ask them to try being the dancing buddy, or to see if they can teach the bird a new behavior or word, something for them to share and then share with the rest of the family if they like. For birds who are deliberately hunting down specific family members to do harm, I think that is a much bigger issue and more to do with environment, routine, hormones and the intricate balance of lifestyle factors which can push a bird to that state than it being a regular risk which needs to be worked around like chunks being taken from a bannister or trying to extinguish that one sound one family member hates.
Wolf: "while providing the means for the child to do so" This is awsome, and so very true. Helping the kid to get a part time job, ensuring that they have resources to do what they need to do for themselves, their bird(s) and their schooling, that is awesome parenting. Responsibility is possible, but it is certainly a much nicer thing if you are set up to succeed.
Perhaps the parent never* cleans a cage, never* feeds the bird, and doesn't buy toys or bird-specific food, but instead helps the kid to get that part time job, has an emergency vet fund up to x amount which the kid can supplement, buys organic veg with the groceries, and helps carry the big cage outside when it gets stuck in the door. Yay. But they also need to be willing to help directly when supplementing is not enough - when the learner driver needs to take the bird to the vet past their legal driving time (don't think USA has this, but some countries don't allow learner drivers to drive at night without a fully licensed driver accompanying them), or when the vet fund is depleted, the family can handle it, and vet care is still in the bird's best interests, or when the kid gets a scholarship to a short program overseas or in set housing and the *parent has practiced stick handling and is skilled with care, though they never normally need to use those skills, and can take over safely without being overwhelmed, for example. I think that is all a part of setting the child up to succeed at committing to such a big responsibility.