In fact no other royal kids are photographed outside these days, other than in the 1990s, unless the palace allows a photocall!
You won´t normally see the royal children from Denmark, Netherlands, Norway or Sweden just passing the streets or playing somewhere. All the photos we see of them, are more or less staged (the Lech holidays of the dutch Royals, Ingrid and Magnus of Norway at their grandparent´s silver jubilee, the King and Queen of the Belgians bringing the children to school after their summer holidays, first little "engagements" of Christian and Isabella of Denmark, 1st day at school etc etc.).
Photographers are allowed to attend these events to leave them completely alone during their private lives in return.
What makes the Cambridge´s so special? Well, they´re of course not more important or precious than other royal children. But other than their continental counterparts, they´re not just popular in their country, but, small as they are, some sort of "world celebrities", no matter if their family or we like it or not. In that regard it is only fair for their parents, to be very much aware and protective - I in William or Catherine´s place would do the same thing!