Quite simply, the White House was built as a symbol of the government. Before the official move to Washington D.C, there had been multiple presidential mansions in both New York and Philadelphia. While today we might think that it's contradictory to be against kingdoms but have "pseudo-palaces", the whole point were that they were government residences, occupied only when you were the president. While a very large perk, it basically forces the president to act as though the country is watching his every move, because, in a way, it is.