I doubt very much that anyone picking up his child at school has an armored car. It's not as though all the parents are billionaires living in deadly fear of kidnappings.
I think there is actually a bigger question: Why can't the President live in the Casa Rosada? Then he would be right there where he works every day, same as the President of the US. WHY should taxpayers maintain a mansion in Zona Norte - and it's a mansion that the public absolutely never see. It's closed to the public and you never even see photos of events that take place inside. At least the public, even foreigners, can tour the White House. For that matter, even Buckingham Palace is open to the public - but the Presidential house in Argentina is above all that. It's one huge waste of public money. Get rid of it (the land alone is worth a fortune and could be developed) and there will be no need for daily helicopter rides to and fro. It will also help to eliminate some of the elitism that plagues the country.