Because the question arises frequently for a historian of Chicago’s built environment, particularly in comparison with Manhattan, I’ve done hours of research on this subject—perhaps more than anyone else studying urban morphology—but have only come up with my own (informed) conjecture on the subject. In short, I think alleys were only laid out in 19th century frontier towns where purchasers of houselots might be expected to own and stable their own horses.

Let’s begin by distinguishing rear service lanes (which we’ll call alleys) from minor streets, which of course have been around for millennia. (The Wikipedia entry does not distinguish, and someday perhaps I’ll wade into that swamp.) When 19th century cities were laid out with large blocks, landowners often cut new streets through the blocks to allow sales of smaller lots. You see this pattern on Philadelphia's Society Hill, in San Francisco's South of Market blocks, in the very large blocks of Salt Lake City, and elsewhere. The most studied example is Washington, DC, where "alley dwellings" became home to freed slaves and by the Depression were desperate slums.

What seem to be America’s first alleys are the ones that James Oglethorpe included in his 1733 plat of Savannah (Georgia), but the feature doesn’t appear to have been taken up by other town plans of the era. L’Enfant’s 1792 plan for Washington doesn’t include alleys (nor had its colonial predecessors Georgetown and Carrollsburg). Not all towns of the era can be examined so closely, but alleys don’t seem to have been a part of Louisville (1779) or Cincinnati (1788). Pittsburgh (1784) has a more complicated history, and it isn’t clear if certain narrow streets were intended as minor streets or service lanes. A 1792 map of Baltimore shows alleys through some newly platted outlying blocks. But . . . by 1815, the alley seems to be commonplace in new towns appearing on the nation’s frontier. In Ohio, Zanesville’s 1815 plat includes alleys, as does Columbus in 1817. The idealistic L’Enfant–influenced plans for Detroit (1807) and Indianapolis (1821) include alleys. The 1835 law authorizing the platting of Chicago says it’s to be “subdivided into town lots, streets, and alleys,” suggesting that’s the expected practice for new townsites.

And right in the middle of this era, the 1811 Commissioner’s Plan plats the entire island of Manhattan—with no alleys. Marguerite Holloway's book The Measure of Manhattan simply says (p. 146) that "no provisions were made for rear alleys," and the Commissioners’ own notes are silent. Clearly the concept was by now well-known, so I think the most likely theory is that they were expecting a compact port/mercantile city rather than one strongly connected to a rural hinterland, whose residents might be expected to frequently travel using their own horses. I suppose we should note that what we today see as the big issue for alleyless Manhattan—garbage bags and cardboard cartons piled on the curb at night—wasn’t all that much of a problem in the 19th century. Much organic refuse fed nearby pigs or chickens, while the occasional crate or carton could be reused or easily burned on site much of the year. Cities around the world developed many solutions other than rear alleys to the problem of storing and removing refuse.

Alleys were a casualty of the auto age, which allowed houses to be built on such large lots that there was room for a side driveway. The expectation that snow would need to be cleared from driving surfaces meant that alleys were expensive to maintain as well as to build, so in the 1930s and 1940s they disappeared from most new subdivisions. A curious exception was Dallas, which continued to require them; some Dallas suburbs do as well, seeing front-loaded garages as an image they want to avoid.

There’s precious little written about alleys, alas. The most useful resource for looking at historic town plans in America is John Reps' The Making of Urban America. There’s been some scholarly writing about Washington’s alley dwellings, such as James Borchert’s Alley Life in Washington: Family, Community, Religion, and Folklife in the City, 1850-1970. Grady Clay did a little booklet about Louisville alleys as part of the city fabric and renewal efforts, but it says little about origins. The most prominent book for modern city planners on street layouts, Streets and the Shaping of Towns and Cities, by Michael Southworth and Eran Ben-Joseph, says very little on the subject. I helped with a radio feature for Chicago’s WBEZ on Chicago alleys past and present.

Follow up question. What did people do with their poo?

While we can't know the exact thoughts of the Commissioners, I'll try to frame the question as closely as possible.

Firstly on the Commissioners' plan itself. The Assembly had tasked them with with laying out of "streets, roads and public squares" in such a manner "as to unite regularity and order with public convenience and benefit, and in particular to promote the health of the city" by allowing for the "free and abundant circulation of air". (as quoted in Gotham: A History of New York City to 1898, Burrows and Wallace).

The first things mentioned are "regularity and order" and "public convenience and benefit". Up until around 1800 development in New York City had been organic, with streets developed privately that later fell to the City to care for. This was starting to become a real mess. The city itself also wanted to sell its own land (mostly in the middle of the island) and this couldn't be done unless there was a clear way to access it. So the primary need behind the plan was really to create a structure of major connecting roads across the island. There was a previous attempt in the Mangin–Goerck plan (1799) that failed to get the political impetus it needed to happen.

Secondly from the quote above you can see the description of sanitation. It was indeed a major concern, but the answer was seen as "free and abundant circulation of air", which is very much not narrow alleys.

For why this is the case you probably have to look at New York's sanitation at the time. This was a time when New York City was seen as a particularly unsanitary city, particularly compared to European cities of the same size. There had been many outbreaks of yellow fever particularly. Domestic pigs roamed the streets and dead animals could sit on the streets for weeks or more without being moved. (My favourite description of this is the pithy writing in Bernard Rudofsky's Streets for people). It wasn't until 1893 that both street cleaning and garbage collection became significant. (For reference, here is a famous Harper's Weekly issue comparing streets in 1893 to 1895). In the early 19th century it was very much the individual landowner's responsibility to deal with household waste either on-site or through paid collection. Connecting the dots, I would expect the Commissioners would have seen a small alley as another place to fill up with waste and need cleaning rather than a tool to keep an efficient waste collection system going as we might see it today.

Its worth also noting that most of the cities being developed with alleys were being planned afresh in this era, which would have given quite different drivers to their planning than those in New York.

Follow up question. Did any city plan include alleys?

Follow up: how was it built without alleys?