Most of New York City's subway system was privately owned until 1940. Why did the city obtain control over the lines at that point?

Prior to the city takeover, there were three distinct lines: the Interborough Rapid Transit Company (known as the IRT, which included the original underground subway system that opened in 1904), the Brooklyn Manhattan Transit Corporation (it was originally known as the Brooklyn Rapid Transit Company, which was incorporated in 1896; it was reorganized and renamed after the deadly Malbone Street Wreck in 1918) and the Independent City-Owned Subway System, (later called the Independent Subway System, the IND, which was the city owned and operated line). A previous agreement, called the Dual Contracts, was signed between the IRT and BRT in 1913, leading to a massive expansion across the city; one of the most important conditions (in terms of later unification of the systems) was that any sections built by the city could be “recaptured” and run by the city.

New York City Mayor John Hylan first suggested a unified subway system in 1921. Hylan (who previously worked as a motorman for the BRT, a position that he was fired from, leading to a personal vendetta against the private subway companies) recommended that the city take over the IRT and BRT lines, also suggesting that the city construct its own subway line. The first step towards eventual unification was the creation of a Board of Transportation that would construct an independent line and oversee operations. Previously, the city’s subway and el lines were coordinated by the Rapid Transit Commission, which had been organized in 1875; in 1907, it was replaced by the Public Service Commission. The Board of Transportation, restricted to controlling the city owned system, began operations in 1924, and in 1925 ground was broken for the 8th Avenue subway, which opened to great fanfare in 1932 (the same year, coincidentally, that the IRT went into receivership).

The IND lines, originally comprised of two trunk lines, on 8th Avenue and 6th Avenue, were built to the larger specifications of the BMT tunnels. This was significant, as any new lines could be connected to the existing infrastructure later on, which would reduce overall operating costs (the IRT had narrower tunnels and cars, corresponding to the specifications on the Manhattan elevated lines, but the BMT/IND tunnels and cars were built to the specifications of the surface railroads and were therefore larger). The IRT and BMT lines both operated at a loss, largely the result of maintaining the five cent fare for so many years (despite the rising costs of operation, the fare remained at five cents, as raising the fare was a major political issue that many mayors had vehemently campaigned against).

Although unification was Mayor Hylan’s brainchild, it was the colorful Fiorello La Guardia who would oversee the full unification process. Discussions over unification began in 1934 and in 1935 a unification bill was passed, establishing a Board of Transit Control to oversee the process. An agreement between the IRT and BMT was reached, whereas the city would purchase the two lines for $430 million. It was approved by the U.S. District Court, but not the Transit Commission, which argued that the takeover would doom the five cent fare. The issue over the fare was so contentious that La Guardia’s opponents tried to unseat him as mayor, although he succeeded in winning another term. In 1939, La Guardia signed contracts with the IRT and BMT to buy the lines for a total of $326 million (the stocks of the two companies fell after 1937). Unification would go into effect in June 1940 (the final contracts were signed exactly thirty six years after Mayor McClellan officially inaugurated service in 1904).

With unification, the subway system had over 781 miles of trackage, 437 miles of street railway and 79 miles of bus routes (the trolleys would sadly be completely phased out by 1960). One of the immediate effects of unification was the abandonment of several sections of elevated lines in Manhattan (the last of the Manhattan els, the Third Avenue line, hung on until 1955; the northernmost section in the Bronx was abandoned in 1973). Several of the Brooklyn els would soon be taken down too. The five cent fare survived unification, but would be increased in 1948 after high operating costs resulted in an $18 million deficit; in 1953, the fare was raised to 15 cents, leading to the creation of a dedicated token that would fit in the subway turnstiles (tokens were phased out in the 1990s, with the last ones sold in 2003).

I hope that answers your question. I will be compiling my sources into a separate comment that I will post shortly.