Not many but a lot of that has to do with the available utility of a 40 year old car with a 40 year old engine.
A lot of 40-50 year old planes have a new or FRM engine somewhere along the way which would effectively be dropping a 0-mile engine into the 40 year old car.
There are plenty of reasons people dont do this for cars... Cost is chief among them. The cost of the new engine vs the cost of a new car isn't that wide of a spread. Add in the fact that a new car comes with new paint, new interior and upholstery and the cost of "renewing" a 40-year old car runs about the same as buying a new car. Second is feature set. Cars are constantly being redesigned. Seatbelts weren't mandatory in the US until 1968, other safety features didn't become mandatory until much later and there are plenty of other safety features in cars today that still arent mandatory but desirable (lane-assist, dynamic cruise control, brake hold and auto braking). That's just safety features... Then you get into the "creature comfort features." Heated seats and steering wheels, GPS, Satellite Radios, adjustable performance profiles, etc. Last you get into the nice to haves such as Distance-to-empty monitoring, better gas mileage. It all adds up to being more bang for your buck to buy a new car than it is to repair an old one. Can you say the same about an old airplane?
At the end of the day, all that really separates a refinished 1940's cub with a new carbon cub is the panel, the overall weight and the cost which is often a fraction of new (though in the case of the 1940's cub due to demand, the 70 year old plane can often run as much as if not more than the new plane). A 1970's C172 with a run-out engine and worn interior could be purchased and made practically "new" with refinished interior, new paint, new FRM engine and upgraded avionics for half the price of a new one. If the same could be said about cars, there'd probably be a lot more 40+ year old cars on the road.