Why do NASCAR drivers have to stay in shape?  

You do have to be in good shape to drive a race car. For one thing, the car isn't going to go in the direction that you want it to all by itself and it's not that easy to steer. There is also a lot of stress put on your entire body, especially during long races. And don't forget those pedals that have to be pushed and sometimes held over and over again for long periods of time.

driving a car for 500 miles at 180 MPH is hard work and can wear a person out, you can not do this and sustain the heat and what it does to your body without being in good shape.

The cars are heavier than the car you and I drive, it is estimated that when a driver makes a turn (most races there are four turns) he faces 3.2 G's.. Imagine that if you can

add in the heat on the track, they say that if it is 80 in the stands the track itself is about 125 to 150 degrees. their is no aircondition in the car, the drivers well do not get a bathroom break and are given small amounts of liquid during the races.

do that without being in shape

being in a car going almost 200 miles per hour, sweating, hot, no a/c in the car, arms have to be strong to hang on to that steering wheel for hours upon hours and legs have to be strong to keep on the pedals and in one position for hours upon hours. They also have to keep their bodies in shape so they have the stamina and energy to keep awake, and deal with the heat from the track and the car and stay on their toes to know what is wrong with the car and go for that checkered flag.
they can't eat before they get into the car or during the "rain" delays if their system isn't used to it, with the heat and stress of the car they could get sick and choke. that would not be good for a driver. there is alot more than just driving.