Because the statue represents a goddess, and goddesses are worshipped. We know she's a goddess. Her ideal proportions, her majestic garments, the torch she carries, and her colossal scale are indications of that.
Furthermore, she stands on a pedestal. Mortals don't stand on pedestals. It might be the case that Lady Liberty is our last goddess. Modern science has convinced us that such beings are childish fantasies, and a waste of public resources. Modern statues don't have pedestals. Our pictures have no frames. The idea of a transcendent reality is no more; now every object in the universe shares equal status with every other object. Everything is equally mundane.
But the creators of Liberty shunned the mundane; they lived heroically, and Liberty is evidence of their passion.
The statue originated in the mind of a French statesman, Laboulaye (1811-1883), in the aftermath of his country's defeat in the Franco-Prussian War. The loser in that war was the emperor, Napoleon III; the winner became the German emperor, Wilhelm I. When it came time to decide a new constitution for France, Laboulaye wanted no more emperors. He opted for a republic, and the gift of the statue to the United States was a political gesture designed to nudge French public opinion in the republican direction. A like-minded sculptor, Auguste Bartholdi (1834-1904), was given the commission. The title of the work is "Liberty Enlightening the World."
It is doubtful if Bartoldi's work was ever taken seriously by the cognoscenti. From an art historical point of view he was, in fact, something of a dinosaur. A contemporary such as Claude Monet (1840-1926) is now much better known and appreciated. In the aftermath of the war that inflamed the patriotism of Bartholdi, Monet went to England and to Holland, where he painted windmills and canals, subjects that might appeal to the tourist or vacationer. Later, he withdrew a bit further, and concentrated on haystacks. Finally, he did waterlillies. But he wasn't really painting waterlillies: he was painting countless impressions of blue and green and gray that, for some reason, took his fancy.
When we compare Liberty to Monet's paintings, it's hard to believe that their creators were fellow citizens and contemporaries. Most of us have forgotten the name of Bartholdi. But the boy in Iraq and the students in China are not waving posters of haystacks and waterlillies.