DC sent through central London private schools so bodyguards were not unknown - often referred to as "drivers".
I occasionally chatted to one whilst his charge was swimming. He was very pleasant, with some sort of military background He was always careful positioned so he could see both the girl in the pool and people coming in and out of the leisure centre, and I doubt he missed much. He said he got on well with staff, and particularly the Head, at the girls prep school, but that though he was present at every sports day, concert etc, many of the mums blanked him. But then you don't talk to staff! He once muttered something about how he wished they would all hurry up in the changing room (a standard complaint) as he had to take the girls dad to the airport at 5.00 the next morning, so it seemed a pretty full on job. I think both parents travelled a lot so he de facto spent a lot of time with the girl. He said he would miss her when she went to boarding school.
I heard that a local spectacle was Abramovich children leaving nursery school. Car pulls up outside, two men go in and physically carried the small child out. I did not hear about them being followed from class to class. The boy used to take the train to secondary school, albeit with two body guards nearby, and whilst a friends daughter went to some sort of awards ceremony with one of the girls and the Abramovich provided a limo (with picnic) to take the girls from one building to another rather than have the group walk outside a short distance.
There was a boy in DDs year who had "a driver". Again I doubt the bodyguard went to lessons, but he did pick up nice lunches so the boy and his friends could eat in the limo as an alternative to school dinners. DD thought that was cool, but never got invited.
The seriously rich kids were not envied. A lot of planning was needed to give them a "normal" life. The average teenager could work out that freedom, and not being at risk, was more valuable.