I've taught many children of famous people.
In my experience it goes one of two ways.
- Children are an accessory to parents' lifestyle. They get moved around the world/country on a regular basis, have disrupted schooling, lots of tutors and nannies coming in and out of their lives, etc. Parents rarely if ever come to school events or parents' evenings. Parents have made it very clear that the child will never need to work and therefore don't need to be arsed with school/getting qualifications. There is very little routine/structure for the kids and no accountability for poor behaviour or achievement. They are exposed to their parents' fame in an unhealthy way (taken to premieres, photographed, papped, plastered over social media, etc) and are surrounded by celebrities all the time, making any semblance of a 'normal' life impossible. These children invariably end up doing very poorly at school and drift afterwards because they don't know who they are beyond being 'famous person's child'.
- Children are kept well out of the limelight and have as normal a life as possible. One parent is usually totally non-famous and always at home, so if the famous parent is working away, the children's routine doesn't change. Parents have made it clear to the children that they will not be getting a meal ticket for life and need to make their own way in the world. The children are expected to work hard at school and do well. Parents are very involved in school life and always attend events and parents' meetings. The children are never taken to any event where they will be photographed and they are kept out of the media circus entirely, including never being mentioned in interviews, so sometimes the children's' names are not even in the public domain. Their day-to-day lives are quite ordinary (but still privileged, of course) and they are rarely if ever in an environment where they are surrounded by celebrities. These children tend to do well at school, have healthy, stable friendships, and go on to do all sorts of degrees and jobs, often not connected to their parents' careers.
From the outside, the children in the first group seem like they have an absolutely amazing life - living in a string of mega mansions all over the world, holidays on yachts with movie stars, people falling over them to give them whatever they want, whenever they want - but the reality is, they have no stability and no purpose, and often struggle with making meaningful relationships as they never know if people like them for who they are or for who their parents are. Their parents' fame means they are just an extension of their parents, not people in their own right. It's also really hard to ever feel a sense of pride or purpose when it's unlikely you will ever live up to the success of your famous parent/s or be allowed to have credit for your achievements. A lot of these kids are very fragile and troubled as a result of their parenting and as they get older, self medicating through drugs and alcohol can become a real problem. Even when these kids have been a nightmare to teach, I've always felt really sorry for them. It's not a childhood I would want.
The children in the second group tend to turn out well because their needs have been prioritised by their parents throughout their childhood, their life is not built around their parents' fame, and they have been given a secure and stable start in life, surrounded by normal people, so that they don't exist in an alternate version of reality in which everyone is a super wealthy celebrity.
I would imagine the Beckhams' children fall into the first group of celebrity children and that being their child is not easy. Misogyny means that people want to blame Brooklyn's wife for his choice to separate himself from his parents - just like people want to believe that Meghan Markle poisoned Prince Harry's relationships with his family - but I would imagine that meeting someone and being able to form his own family has given him the ability to step away from a very controlling and limiting environment where he was just another product in his parents' brand catalogue. Good luck to him.