I can't answer for Cleveland, but I can explain how an equivalent process happened in the UK.

Between the 1930s and the 1950s all the UK tram networks ( the UK term for streetcar) closed, the sole exception being Blackpool in the northwest of England.

There were 2 main causes. Firstly tramways were obligated to maintain the roads in which the rails were laid that the trams ran on. This was a substantial extra cost that the motor bus companies did not have. Roads away from the tramways were funded by local and national taxation. This made tram networks expensive to operate, and although they had advantages in terms of energy efficiency and load carrying over buses this did not offset the fixed costs.

Secondly most tram systems developed n the early years of the 20th century. After 30 years equipment was becoming life expired and capital investment was needed in vehicles track and electricity supply. The cost of replacing the network with motor buses was often lower.

There were other reasons, although they were probably less critical. The UK government promoted the bus building industry after the Second World War as it was seen as a vital export industry and having a robust domestic market would support that. ' Bury your trams with Leland buses' was an advertising slogan of the time.

Town planners regarded trams as impediments to the free flow of traffic.

Trams work best in areas with high population density. Slum clearance, new housing estates and urban sprawl all made the existing networks less viable.

Much lower operating costs.

Streetcar lines had the enormous expense of maintaining track and overhead wire, and often their franchises obligated them to pave and clean any streets where they operated. By the 1910s, this meant they were providing a smooth clean roadway for their competition: the private auto, including car owners who would offer rides for a nickel to waiting streetcar patrons (operations that came to be called jitneys, from the period slang for a nickel). In addition, buses could be run with one man, while labor contracts at many companies required two men (a motorman to drive and a conductor to collect fares) on streetcars.

By the 1930s, most private traction companies faced worn-out equipment, worn-out track, and (sometimes) labor contracts requiring two-man operation. In one fell swoop, they could take care of all those burdens by substituting one-man buses. In virtually every case, the public hailed the new buses for the smoother ride and quieter operation they offered. Buses were also more flexible for getting through and around traffic, which had been growing rapidly, even during the Depression. All those cars made it harder for streetcars to get through, and they made it dangerous for passengers to board in the middle of the street. Buses could pull to the curb.

The McGraw Electric Railway Directory for 1924 lists 955 electric railways in the United States. By 1975 there were only seven streetcar cities left in the US: Boston, Newark, Philadelphia, Pittsburgh, Cleveland, New Orleans, and San Francisco. The Census of Electrical Industries provides some useful numbers for how steep the decline was in the 1930s. The number of street railway companies was 963 in 1927, 706 in 1932, and 478 in 1937. Streetcar companies in the US were often cross-subsidized by real estate ventures, or had the backing of electric utilities. When the 1935 Public Utilities Holding Act forced electric utilities to divest their transit franchises, the new owners desperately needed to cut costs, and that was often the last straw for the streetcars.

One can’t discuss this topic without someone mentioning the National City Lines conspiracy theory. I’ll point to our previous discussion of that. It’s also worth noting that virtually every city around the world followed exactly the same course the US did, and streetcars disappeared from virtually every city in Japan, Australia, China, Korea, India, Africa, Spain, France, Italy, Great Britain, Canada, Mexico, and South America. A sober debunking of the NCL conspiracy is found in Slater, Cliff "General Motors and the Demise of Streetcars" Transportation Quarterly, Vol. 51. No. 3 (Summer 1997). This article is online as a PDF.

Some sources for further reading on this topic:

Bottles, Scott L. Los Angeles and the Automobile.

Barrett, Paul. The Automobile and Urban Transit: The Formation of Public Policy in Chicago, 1900-1930.

Jones, David. Urban Transit Policy: An Economic and Political History.

St. Clair, David J. The Motorization of American Cities.

Yago, Glenn. The Decline of Transit: Urban Transportation in German and U.S. Cities 1900-1970.

I can't speak about Cleveland's history, but I can comment on the similar evolution of Southern California's transportation system. Many people believe that the car companies conspired against the streetcars in some underhanded way (see: "Who Framed Roger Rabbit?"), but its more boring than that.

It's true that SoCal had an extensive streetcar network in the early 20th century. By some measures it was the world's largest urban rail system. Before cars became affordable (and therefore popular), it was the most efficient way to get around a region that was very spread out.

So why didn't it last? Two main reasons. The first is that the streetcar systems were not government-run. They were privately owned. Like many companies, they often sacrificed quality of service in the name of profits. Riders complained about streetcars running late, breaking down, running people over, being noisy, etc., but the riders had little recourse. Imagine that your commute was at the mercy of an entity that was even more unreliable than your cable company, only instead of throwing a fit at the cable company's office or negotiating a new price package, nothing would happen at all. And local politicians couldn't really help because the streetcar companies had bought them off. At times the streetcar companies made more money on real estate development than fares because they built stations to serve the housing tracts that they themselves built and profited from. The Los Angeles sprawl that cars get blamed for was originally the product of streetcar-dependent towns. You'd buy a cheap house in the country and then were dependent on the streetcar company - who sold you your house! - to commute to work. So many riders were irked at how corrupt the streetcar companies were, and how their local monopoly status allowed them to stay complacent about serving their riders well.

The other reason the streetcar system deteriorated was that they conflicted with the growing road system in ways that caused traffic jams. As cars became more popular, the roads had to cross the rail tracks more and more, which caused congestion. (Grade separations like bridges and underpasses were too expensive and impractical to build most of the time.) Car owners who had paid a lot of money for their new wheels resented the streetcars for slowing things down. Since the streetcars weren't publicly owned, there was no communal support for them. As commuters switched to cars instead of riding streetcars, streetcar revenue dropped, which meant less was spent on maintaining the streetcars, which encouraged more car buying. You can see where this is going.

By 1930, the streetcars were pretty much just in the way. SoCal embraced car ownership before most other parts of the country did, decades before any conspiracies to replace streetcars with buses or to tear up tracks. Privately-owned mass transit tried to compete on price and customer service and failed spectacularly.

As the OP points out, it's ironic that rail is making a comeback. But the people who think SoCal's original light rail should never have left are wrong. For a little while it was ahead of its time, but without a public mass transit network or dedicated right-of-way, it was doomed to fail.