It's getting very difficult to purchase a manual transmission in the US, let alone rent one. About the only cars where a manual is still offered (they used to be called 'standard' transmissions, because automatics had to be special order) are the high performance (and expensive) cars like Mustang, Corvette, Viper, etc., and on the lower end of the price range, like a Ford Focus. Most of the cars favored by rental companies, the so-called mid-size or full-size sedans, aren't even offered with manuals by the factory. Out of all the cars sold in the US recently, about 6-7% came with a manual. As mileage and pollution regulations get stricter, the manual might go the way of the dodo in the near future. With 8-speed automatics becoming available, cars get better mileage than with a manual gearbox and since the engine is always under load, less pollution is emitted.
At least with US driver's licenses, you were free to operate either an automatic or a manual transmission, unless you had some physical disability which prevented it. I had learned to drive an automatic and practiced a little on manuals, but was not smooth clutching by any means. When I bought my first brand new car (a 1984 Camaro Z28), I specifically ordered the 5-speed manual because the automatic in those years was relatively fragile and unreliable. It took me a while to get the hang of shifting, especially in city traffic, but the gearbox never had a problem in 15 years of daily driving.