For starters, the steam car did not remain commercially viable into the 1920s. The three main steam car manufacturers in the US were Locomobile of Bridgeport, CT; Stanley of Newton, MA; and White of Cleveland, OH. Locomobile switched to internal combustion in 1903, and White switched in 1910; only Stanley remained committed to the powerplant, and by the mid 19-teens was producing just a handful of cars a year. They limped along until 1924 before folding.

So why was the steam car popular? You're absolutely right about the water consumption- a non-condensing Stanley got approximately one mile per one gallon of water, with a forty-gallon tank. But steam propulsion was relatively smooth and vibration-free, required no transmission or gearbox, and could not be stalled. At a time when the average ICE Automobile had a 1- or 2-cylinder, 10 hp or less engine and just 2 or three speeds, the immense torque generated by a steam engine could conquer any hill and accelerate faster than the competition (even today, a Stanley with a full head of steam can beat a modern car off the line). Steam car agents and dealers played up that their automobiles were based on a proven technology that had been refined over the previous century, and even referred to gas engines as "internal explosion engines" to play up the unreliability and unpleasantness of contemporary ICEs.

The heyday of the steam car peaked in 1906-1907 - during those model years both White and Stanley hit their peak sales output, and in January 1906 Fred Marriott set the automotive land speed record at 127 mph driving a customized Stanley at Daytona Beach, Florida. That year, Theodore Roosevelt became the first president to drive an automobile, getting behind the wheel of a White steamer while in Puerto Rico.

America Adopts The Automobile by James Flink is a great, if slightly dated, overview of the formative years of the automobile industry.