In the United States, how many new suspension bridges have been built since the Verrazano opened in 1964?
Except for the twinning of the Delaware Memorial and Chesapeake Bay bridges, I'm not aware of any. It seems like most new longer spans prefer the cable-stayed model.
So it appears that the engineers have decided, for whatever reasons (economic and practical) that suspension bridges are only to be built for especially long spans. And the Verrazano remains the longest single-span in the Western Hemisphere (corrections welcome). Other suspension bridges have since been built in other parts of the world, but most if not all have longer spans than the Verrazano, starting with the UK's Humber Bridge in 1981.
If New York's East River were being spanned today, the Williamsburg and Manhattan Bridges would probably be cable-stayed. I would say the same thing about the George Washington, but -- can a cable-stayed bridge handle 2 decks of traffic? Twin spans seem to be the preference where there's heavy traffic demand. Note: there is a double-decked, cable-stayed candidate for the Brent Spence Bridge replacement (I-71/I-75 between Cincinnati and Kentucky, Ohio River), but that is just a concept drawing.