"The confetti drop started in 1992, when it was intended to lighten up the tone of the event. “Up until that point, it had just been a drunken brawl,” said Treb Heining, who managed the confetti that first year and has been doing it ever since. “It was so seedy.”"
I think they are attributing too much to confetti -- how does one minute of dropping paper at the end of the event transform an hours long event to something less seedy? I think the big push to clean up the Times Square area that started around then is the real reason the event became less seedy.