Apparently, Houses in several different places (such as Amsterdam during the 17th century for example) were at some period in time taxed by their width. House styles in such places seem to have evolved into very long and thin houses in order to minimize taxation.
I have come across this idea in several European and Japanese cities, mostly in regional trade hubs and harbor towns so I believe there must be an economic reason that made several places choose this form of taxes independently of one another. But what is that reason?
Was it the inability to reliably measure the square area of a building? Was access to the road the actual basis for taxes and by having merchants minimize their roadside exposure, more merchants could trade on the main roads thus generating more revenue for the city?
Yup. Access to the road. The road is the real expense for the city, so that way they get the same revenue per distance of road no matter how many properties are on it.
You'll notice how even without taxes set up that way, housing tends to go in that direction. Look at row houses in any high-density city. Or you could look to the "skinnies" in cities that are in the middle of moving to higher density (I'm thinking Portland and Seattle). Your house needs street access, so when a lot gets divided, there's only one line you can use to split it.