To be surrounded by a gaggle of photographers and onlookers when a kid is being just a kid isn't interacting with their "subjects". To be the center of attention among a huge gathering of people because of who one is, for a kid, is scary. Events like this past one where people say it would have been nice to see the Cambridge kids, I think, would have been confusing for the little ones, a handful for the parent in charge (as has been pointed out) and basically, the kids at that age have short attention spans and really don't know what polo really is from a hill of beans. The Cambridges opted out of bringing the kids. William was there for a reason. That's totally fine with me.
To grow up in a "normal" environment interacting with other people and especially children their own age is a horse of a different color. Its not appearing in public that does it. George and Charlotte will learn from events like Trooping the Color and being on the balcony bit by bit what their family role in the scheme of things are. The important things are their interactions with other people by going to school and the other everyday things that build up a child's social world.
To grow perhaps to want to take on roles of service as their father and their uncle did by watching examples. Daddy was a helicopter pilot to help save lives. Uncle Harry was a soldier and now works to help sick soldiers. Mummy does a lot of things for little kids that need it. Even eating dinner as a family in the kitchen and sneaking those vegetables under the table to Lupo is what is more "normal" than kids eating with nanny in the nursery while Mum and Dad dress for dinner and are served a five course meal.
The desire for Cambridge kids to grow up "normal" and not behind palace walls, to me, simply means that some of the old fashioned rules and regulations of raising kids have had to be discarded. Emphasis on being a family for the little ones take priority. Going to school and interacting with other children is crucial to building social skills. George and Charlotte as little people are the priority and their prince and princess roles are their destiny in the future. Its important to the Cambridges that the children develop as little people first then grow into the prince and princess roles when the time comes.
Having them out and among the "subjects' and getting photographed and followed around and all attention on them could very well be detrimental to their development as too much of that could give the kids the impression that they are special among ordinary and they're more interesting than ordinary and that they're always seen as being "above" ordinary. So, it doesn't surprise me in the least that Kate and William want to keep this to a minimum.
Raising a child to have an "ordinary" ego starts with keeping things simple and ordinary from the start. At least that's how I see it.