I think if kids are shown the value and the beauty of learning something, bribes are necessary.
There's a great book I read when our son was born titled "The Scientist in the Crib". The gist of the book is that kids are wired to learn, and there is some editorializing that traditional school systems unplug that natural wiring through a continual flow of punishments and rewards.
When I offer our son a reward, he isn't motivated. When I show him how cool something is to learn, you can't stop him from pursuing an activity.
Sorry, but didn't you mean "bribes are NOT necessary" in your first sentence above?
About your other paragraphs, I agree with you completely. I was about to reply to your other thread in Studen'ts Corner about beginner or return adult ... very interesting, but my reply became a whole novel I've better polishing it first ...
Well, but the essence is that there is a fantastic mechanism behind learning that our school system and "traditions" effectively kill. We are all born with this mysterious talent. We all have an inner drive to explore, to grow, to make a change. And as adults we are amazed by the determination and diligence a little child has when it learns to walk, for instance. And other capabilities - here in Piano World we talk and talk about "brain plasticity" and other aspects that should explain why children can learn to play the piano so fast while an adult has to struggle. We even tell each other that it is impossible to become real good at piano playing unless you start at kindergarten age, because when you are 6 your brain undergo certain changes and when you have passed 15 you are literally so stiff in your mind that it is a wonder that anyone can learn anything after that age ...
Sort of. Of course it is highly unscientific baloney.
Our present educational system is not designed with focus on how humans actually work. It was formed in the era of Enlightment and industrialism, where humans and Nature were believed to function just like machines, and the schools therefore were designed just like factories ... with the ultimate goal of producing productive factory workers. Not thinkers, artists or free spirits.
In a factory it is important to classify the products according to certain criterias. When you work with living material, humans, you call it grades and a convenient way to grade people is to let them do this by themselves by letting them COMPETE. We are so brainwashed in this kind of thinking that we think it is natural - look, we say, the animals are also competing when it comes to reproduction. And so we teach our children, when they are very little, that competing is THE thing. We invent games for them which are like little competitions, and we start when they have just about left the cradle. (And before that mothers desperately compete in being The Best Mother by telling each other about their children's progress, so that those who have "slow beginners" will feel rather awkward.)
Well, now look at a bunch of puppies that play. Wolf puppies, dog puppies, they are just the same, the play just the same and you can see that there is a clear goal behind this playing - to learn how to hunt. The race each other, they combat, they tug things. Looks very much like they are competing too, right? NO, THEY ARE NOT. They train to develop as individuals but also as a team. They learn social codes in order to build a team and learn how to cooperate, and they challenge each other in order to become as strong, fast and smart as possible. Because they are pack members, and they will always need each other.
We are also pack animals. We also need each other, and therefore we actually feel good when we can support each other, and we are not comfortable with competitions where one is to win and the rest are to lose, or die, or whatever. That is hostility. That is war. (If you don't believe me, tell me why stress feels so uncomfortable. Because it signals "fight", which is equal to war.) Well, we can all enjoy friendly competitions, were we unite in a higher goal - maybe the love of football? Two good football teams will challenge each other and take out the best of their opponents. Within the team, the players need to cooperate and make the best of their individual strengths and weaknesses. And the people in the audience will probably have their favourite team, but most of all they will enjoy a good game. They can be momentarily heartbroken when their team loses the game, but after a while they will cheer up again and say it was a helluva good game anyway.
That is a good competition, because the competition part is inferior to the love of the sport itself. It is designed to unite, not split. But we all know how it often works in reality ... we create a war instead, full of hatred against the opponents. It could get very, very ugly, because so many believe that Winning is all that matters.
So grown up humans are often far more stupid than puppies in this aspect. And more stupid than little children, because children are just like puppies if you don't "raise" them to believe something else.
Schools, factories, puppies and football. Ok, ok, ok, what has this to do with piano students? Well, everything of course. Rewards and progress charts can be a useful tool, and it can also be a disaster, depending on the attitude you put behind it.
Again, the reason small children learn so fast and older children/adults struggle more is that the small ones have not learned the competition thing yet. They still believe that there are other values that are more important and they are right! I learned to walk when I was just nine months old, because I had an older sister. I probably did not want to "win" over her, I wanted to catch up with her so that we could play, because I loved her. (I still do.) And so I diligently worked on learning the art of walking. I am sure I did not care about praise and rewards from my mother.
When I was five I learned to read. My sister was in school, I was alone, I loved stories and my mother did not always have the time to read for me. I was soo curious about the contents in those books. I remember that Tintin comic album where they talked so much ... and what did they say, really? I wanted to know. So I learned to read, in no time, because I had a clear goal.
When I was six, and still not in school, my sister learned how to play the recorder in lessons after school time. She and her friend used to practice in the evening in our home. I was sitting nearby and I was jealous ... they played their little tunes and learned to read the notes and I couldn't wait to steal the recorder and try it myself because I thought it looked fun, especially when they played together in two voices. Later that year I got my own recorder as a Christmas gift and just a few years later I got a place in the local recorder ensemble, being totally self-taught.
I don't tell these stories to brag about myself. (And it is not much to brag about either.) I do it because I think it shows the power of learning when you are motivated. And hey, I wasn't interested in being better than Him or Her!
I believe a progress chart (or whatever system you have) could be great in order to help children see their progress in moments when they are a little lost. Now, when I am old and wise

I can note my progress my myself so I would just get offended by such external acknowledgement. But a little child may need it.
BUT if used the wrong way, it is a disaster, as I said. I mean, also competitions and ABRSM exams (we don't have them in my country) could be great tools for learning and encouraging, but only when you see them as tools and not as goals as such. Because the major goal should be your love for piano playing, and ever more to share it with others.
If a student, no matter what age, starts to get sulky and depressed because "someone else is better", then you should watch out. This student is on the wrong track and the teacher must help him/her out. The same with a student who just feels bad because he/she did not succeed with the last assignment. In that case, help them find the joy in piano playing again, and help them to truly appreciate the success of others. I would recommend workshops where they can participate in fun music and jam sessions with peers, even if they are ever so "untalented" or unprepared. And always avoid comparison situations. Any pianist's success is every pianist's success. When they listen to an unusually good pianist or student who plays, don't make them sigh and compare this person to themselves. Make them feel that they are in the same community as the excellent pianist. That we are all worthy members of the Piano Lover Pack.