I was reading a book written in 1950 about Stevenson in Edinburgh. The writer Moray Wilson had a very circular style and spent some time scene setting where he suggested Edinburgh was the last place to get rid of Sedan Chairs. He reckoned just before RLS was born in 1850. (In a classic oversight this writer assumes a first world perspective, there is a hospital built in Hong Kong in 1907 where the only way to get there was by sedan chair - this hospital has been running sedan chair charity races since 1975, other places like Egypt and Japan have long history of being carried in a litter).
I can see them lasting maybe just into the 19th century plying their trade up and down the Royal Mile but once the new town was fully built and functional I cannot imagine the overweight advocates of Edinburgh being lugged from Moray Place over to the high court.
However as an antidote to Edinburgh being too hilly for cycling I give you - not really did you know Edinburgh was the last place to get rid of sedan chairs and infact @arobcomp is thinking of bringing them back as an option in his resurrection of his former life in Chariots for Hire.
Quicker than a taxi in the ultra congested streets of central Edinburgh though they do hog the pavements rather.