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"amazing fast" was still decades to fully replace horse and cart and longer for trams and the like and like I said, I'll likely be gone before it happens.
http://www.thecascadiacourier.com/2014/08/from-horses-to-cars-in-seattle.html
"In 1912, traffic counts in London, Paris and New York all showed that the car had overtaken the horse. A Seattle traffic count in 1915 quantified traffic going to West Seattle and showed that horses still held market share in delivery functions but were losing out to street cars and motor vehicles for hauling people. From 5 AM to midnight on that November day, 291 street cars carried 11,699 people, 692 automobiles carried 1,501 people and 203 motorized taxis carried 744 people. Just 155 horse-drawn vehicles carried 187 people."
By the 1920s motor vehicles had completely replaced horse drawn carriages on the roads of New York... By 1925 the price of a Model T had fallen to under $300--- from $850 in 1908 and $500 in 1915.
Keeping to NYC.. and electric cars.. It is curious to note that by 1899 the vast majority of all Taxi cabs were electric. At this time most cars on the road of NYC were electric-- steam had a larger market share at this time than gasoline. It was a double knockout of price (by 1915 an electric car cost as leat 3x a Model T) and range--- to use the emerging highways -- that eventually killed the electric car...
I think it will happen in some places much faster than most pundits expect. While it would take at least 20 years to phase out automobiles alone due to production capacity I expect more affluent urban hubs such as London, Munich, Paris, San Francisco, Los Angeles, Doha,.. to make rather swift transitions. The shift from horses and streetcars to personal motorcars in 20th century was amazing fast. In NYC the paradigm shift took place over just a few years. Just as there was massive political will to "clean up" NYC and replace horses there is massive political will in many countries to shift to electric transport. Individual electric cars have a number of central problems such as range that fleets of shared electric vehicles don't have. BMW, for example, in the context of their electric car development has been busy building a car sharing business ("Drive Now"). German Rail (Deutsche Bahn) has created not just a network of shared bicycles ("Call a bike") but also shared autos (Flinkster). With a German government target of 1 million electric cars by 2020...