The cities didn't commission the views. They were produced by small companies hoping to sell copies of the finished lithographs—though they often got approval of the Chamber of Commerce to make them seem more authoritative. The Library of Congress has hundreds online.

I've heard the claim that war-surplus observation balloons from the Civil War spread this technique, but sketching a city layout or "plan" in birds-eye perspective is not difficult, and gets even easier when it's a regular grid like most cities of the American West. The buildings were sketched from life, later from photos, and then the engravings or lithographs made back in the "home office."

As for accuracy, many details were omitted or just invented. There's also often a lot of wishful thinking, such as big factories that didn't yet exist (always belching smoke), brimming rivers, mature street trees, and a railroad train on every track no matter what time of day.

The main book on this subject is John Reps' Cities on Stone: Nineteenth Century Lithograph Images of the Urban West. The Library of Congress website has this introductory essay, which cites John R. Hébert and Patrick E. Dempsey, Panoramic Maps of Cities in the United States and Canada.

Incidentally, there's a separate tradition of very careful axonometric views of cities going back to the 19th century, and perhaps much earlier in China. This became a mature art under 20th century artist Hermann Bollmann, who produced incredibly detailed drawings of several European cities and (in 1963) of Manhattan. A number of US cities have had axonometric drawings of their central business districts published over the last 25 years; I have three separate ones done of Chicago's Loop.