Why? The war wasn't in 2010. To all indications, it was somewhere around a decade before First Contact, i.e. the 2050s. So a 2009 car would also be an antique at the time.
But it would be an antique that the Kirks would have truly come into contact with, as opposed to a 1965 Corvette. I think that Abrams, Orci, & Kurtzman used a '65 'Vette just because it was more iconic than a 2009 'Vette.