It makes sense from a security standpoint when they knew aircraft would be common overhead soon.
I’ve always thought that it originally had to do with aesthetics more than anything.
In terms of architecture/design, it’s an absolutely beautiful city (even though the advent of Clinton & Co. seriously tarnished my birthplace for me, with regard to atmosphere and connotations.)
When I was growing up, especially in the Summer, it was like a drowsy Southern city. Things started taking off in the 1970s-1980s; and every year it has become more complex (physically and otherwise) and more traffick-y.
Height of buildings may be a security issue now; but keeping them low is also an aesthetic one.