Why do Most Americans Drive an Automatic Gearbox?

You know of course the reasons are quite different.
First, they were the first to mass-produce and mass-sell cars, which brought huge hands-on experience.
Second, the accompanying industry (components, transmissions) followed close.
Third, the country is vast and the fuel (used to be) cheap.
Fourth, the economy and purchasing power were second to noone – while Europe was busy fighting wars, the US kept mass-producing whatever was needed throughout the period – Tin Lizzies, Jeeps or GMC trucks alike. During peace this brought about ever bigger and better-equipped cars with a lot of power and optionals. Gradually the automatic transmission became cheaper to produce and to buy and it spread down to the base models.
European cars can’t afford to waste the little power they get from the engine on traditional automatic gearboxes. Most small European auto-transmission cars were flops from four points of view – reliability, cost, performance and fuel economy.
But the things have changed – check out the recent VW double-clutch gearbox (aka DSG) – it’s an energy-efficient manual gearbox with mechanical and electronic add-ons which seems the way to go. It is compact, cheaper and more efficient than the traditional automatic and gets better mileage than the manual in same conditions. It’s too early to discuss the reliability. As to the control of the car, neither you nor I can beat the DSG in normal conditions – it shifts very quickly and without interrupting the torque flow to the wheels. There may be minor trade-offs in certain conditions (off-road, snow/ice) but even that is simply a matter of time. And believe me, sooner or later most of us get sick and tired of the clutch.
My next car will have a DSG, anyway.