Kirk,
Normally they do but several around here built theirs with Automatics. for one thing their wives like the Automatic and would drive the Cobras. And there are some places in San Francisco that a stick is almost impossible to not burn the clutch out soon. Remember the hill in the movie Bullet? That hill is a real pain to go up when you have to stop at each cross street and then try to start up. I used to set my parking brake, put the car in 1st gear, rev the engine up, and then release the parking brake while at the same time dumping the clutch. Burning rubber like that is normal down there but it is expensive in the long run. However I still prefer the 4 or 5 speeds.
Ron