Actually, the 1960 thru 1963 model Corvair had the same rear suspension. The following year (1964) was the last of the first series car, and by then, Chevrolet did add a transverse leaf to the rear in an attempt to control wheel camber.
In 1965, the second generation Corvair was introduced, and had an all new full independent rear suspension.
Ralph Nader did harm sales of the Corvair, although it has been said that Ford's Mustang also contributed to the cars falling sales.
I have owned a '65 Monza 4-door (shown below), a '63 Spyder Turbo, as well as some parts cars. Wish I still had one.