Just want to add that Charles also went to university, and he also served in the Navy including (eventually) captaining a ship. He would have met and had to lead men from all walks of life.
I think that experience led him to develop the Princes Trust - helping young people who did not have his advantages.
I think he understood that exposure to a wider community was benefical to his children.
To his credit, Charles has made concerted efforts at various times throughout his life to have experiences that might give him a better idea of what a "regular" life is like.
But my impression is that his experiences out in the "normal world" haven't had much chance at giving him a very accurate experience of normalcy. In some cases, like Gordonstoun, he was spitefully held at arms length due to his title. In others (Cambridge, large portions of his Naval career) he was given a very customized/insulated experience, partly in deference to his title, but partly for practical reasons. He had to be available to leave quite often to carry out royal duties. And his time at the university and in the military was first and foremost supposed to prepare him for being King, not really to help him get to know commoners. He has pointedly sought out experiences "close to the land" from time to time, one has to wonder how honest of an experience his hosts actually gave him (and I do think he hoped for honest, warts-and-all experiences)...or how much they quietly edited the schedule of duties because he was a prince. Or because sometimes it's just easier to do certain tasks without unskilled, volunteer "help."
I don't blame anyone for the way that many of his non-Royal experiences were kept relatively artificial. The BRF was feeling its way into new territory with his upbringing. At some point, there has to be a circle of separation between a prince and a greedy world of people trying to take advantage of him. They took a big step by having Charles spend more time outside palace walls at a young age, but built in separations almost as tightly protective (giving him special rooms and a non-standard course of study at Cambridge, for example) which ultimately kept his fellow students and sailors at a distance. Back in the 80s and 90s, Charles used to sound quite bitter about that stage in his life. His own description of seems to be that he was in those places without really being part of the community.
But the BRF seems to have learned lessons from his experience and tweaked their approach going forward. With Andrew and Edward, and then even more so with William and Harry, they have found different ways of building "walls" outside the bounds of their schools or military assignments, so that within that protective circle the princes can still have a somewhat typical experience at their schools or jobs.
It will be interesting to see if William carves out even larger space for his children to move around in relative normalcy, or if his comments simply mean that he wants George and Charlotte to have an upbringing more like his own than his father's.