[taneq]

The answer was "NiCd batteries are way too expensive, lead acid batteries are way too heavy, and both have way too short a cycle life."

[Tossrock]

Deep cycle lead-acid batteries have fine cycle lives, and indeed were (and are) used for driving golf carts. However, they trade off for lower specific power, which makes them unsuitable for a full-sized, highway-speed-reaching car.

[Hasz]

The 2001 Honda Insight was built with NiMH cells -- not quite NiCd, but still doable.