But the children haven't put themselves in that position
No, their parents did, which makes all the "poor Kate, if those were my children..." stuff even more risible.
If she doesn't want her kids subjected to hearing the boos of people who are perfectly entitled to protest and voice their displeasure at an utterly outdated, anachronistic disgrace that she and her kids are very much the living embodiment of, then she can opt out and go live like a normal, albeit extremely privileged, person anyway.
Rather than the endless squabbling about Monarchy vs Presidency etc, how about we simply stick them on an island for 12 months and ignore them completely, give people in the UK a look at what life would be like without them, and then hold a vote on what the institution of HoS should look like going forward?
If the public actually votes for a system whereby we decide to continue to pick a random upper class family, plonk a magic hat on their head, and then inform the citizenry that they are inferior beings to the newly coronated Monarch, and that due to Divine Providence we must then also consider all of their offspring superior and grovel to them and fund their obscene wealth in perpetuity, so be it, bring them back, but lets at least have a full and frank discussion of this being the current status quo, and how utterly ridiculous it is, before we decide to continue on with it.
I'm even willing to leave the Guillotine out of it if the public votes against.