The first mass-produced automatic transmission, the hydra-matic, was developed by GM in the late 1930s. The (hydraulic) automatic transmission is a significantly more complex piece of equipment than the sliding-gear manual gearbox - it relies on complex hydraulic systems and fluid dynamics principles, instead of the centuries-old mechanical engineering principles of clutches and reduction gearsets. Instead of ordinary gear oil, it requires specially-formulated AT Fluid that not only has to lubricate but must run the hydraulic systems. For this reason, automatic transmissions were generally considerably more expensive than manual gearboxes. Until computerization, they were also less responsive and less efficient (early models sent less than 80% of engine power to the wheels) than a capably-operated M/T, requiring more powerful engines to achieve similar performance.

So why did they take off in the US but not elsewhere? Well, at the very outset of the auto age, many jurisdictions across the world implemented horsepower taxes, which taxed car ownership based on engine displacement (a rudimentary measure for both the price of the car and the west & tear it would impose on streets). In Europe these were usually done at the national level; but where they were implemented in the US, it was at the sub-national (often local) level, and coverage was far spottier and less onerous.

Beginning in the 1920s and accelerating after WWII, the US pursued mass-motorization as a policy goal to an extent that is not seen really anywhere else. When people talk about the US as having a “car culture” or “love affair with the automobile” - that is as much a product of deliberate federal policy as it is cultural tends. The federal government pursued policies of suburbanization (for white people) that had begun fairly organically in the late 19th century, expanding the reach of “streetcar suburbs” far into the hinterlands through mortgage subsidies in the suburbs and, chiefly, massive investment in automobile-centered infrastructure. The Federal Interstate system was as much about linking suburbs to city cores (often by demolishing low-income and minority neighborhoods) as it was about linking disparate parts of the country - allowing, and encouraging, middle-class families to live further and further from their places of work, shopping centers, and recreational areas, which would all be linked by automobiles.

The land use patterns that resulted made the US uniquely car-dependent, with far and away the highest VMT per capita in the world. Americans could expect to spend significant portions of their lives behind the wheel, either blasting down wide freeways at 60+ mph or (just as likely) stuck in stop-and-go traffic on those same freeways. The A/T offered a convenience that was uniquely appealing to American motorists sick of clutch-popping their way through a 45 minute rush-hour commute. Moreover, postwar economic boom (and gratuitous federal subsidies) left suburban Americans with the disposable income to afford expensive A/Ts - and the keeping-up-with-the-joneses status symbolism that went with them. Finally, the lack of horsepower tax (and cheap fossil fuels) meant that the efficiency losses of the A/T were fairly trivial - you could simply increase engine horsepower to compensate.