Lots of cars around in 1871. I think grids are useful layouts for cities that don't have any motorists. Most of these gridded cities were designed before cars. Modern suburbia loves the cul-de-sac.
I was thinking of natural structures like the branches of trees and the tributaries of rivers. Because cities rebuilt like that in the 20th c does not mean that it was a good idea or successful.
A gridded street system is also quite useful for inhabitants/businesses that want to go to an address without a map (or even with one). You can easliy go to a place you have never been to before. This is probably a highly undervalued property of grid layouts for cities before the invention of telephones, GPS, etc.
Cities that had the opportunity to rebuild (like Chicago after the 1871 fire) make use of grids.