The public transit system of Baton Rouge (the Capital Area Transit System, or CATS) is underfunded with routes in an older hub-and-spoke model. How did it get this way? When did it start and why is it now essentially government-run?

Population of Baton Rouge city and parish, 1810-2010
From what I can tell given the sources available to me, the story begins in 1881 when the city of Baton Rouge had a population of 7200, the parish had a population of 20,000, and there were rumblings of creating a streetcar system. So let's start the timeline there.
October 11 — Baton Rouge Street Railway Company charter filed1
November 11 — Baton Rouge Street Railway Company franchise purchased from City of Baton Rouge but fails to produce anything because funds could not be raised 1
November 10 — William Garig (a very rich white guy with a house at 243 Lafayette St.) tried a second time to start a street railway by travelling north to find investors; Baton Rouge Street Railway (BRSR) chartered in Suffolk County, Massachusetts ref ref 1
March 21 — franchise ammended and assigned to J.A. Andrews, J.N. Ogden, and H.W. Ogden 1
? — Baton Rouge Electric Light and Power Company brought electric lights to the city ref
? — Baton Rouge Electric Light and Power Company amended charter to be named Citizens' Electric Light Company ref
October 16 — streetcar started operating 1
October 22 — Baton Rouge Railway & Improvement Company (BRRIC) chartered, planning electrification; took over BRSR 1
September 22 — Capital Railway & Lighting Company (CRLC) chartered in Baton Rouge as subsidiary of Fort Wayne Electric Company with the goal of purchasing BRRIC and Citizens' Electric Light & Power Company ref 1
November 5 — entire property transferred from BRRIC to CRLC 1
November 15 — CRLC absorbed Citizens' Light & Gas Company (indicating how closely tied streetcar and electric service would become) 1
April 6 — electric streetcar service started 1
June 1 — Home Electric Company, a new local company, chartered to purchase CRCL property 1
June 20 — Baton Rouge Electric & Gas Company (BREGC) chartered to purchase all electric, gas, and railway property in Baton Rouge 1
February 14 — Stone & Webster Engineering Corporation, national holding company of railway systems, bought BREGC 1
August 9 — Baton Rouge Electric Company (BRECO) formed by Stone & Webster to take over BREGC 1
January 30 — sale finished of BREGC to BRECO 1
? — BRECO bought 3 buses for service between downtown and LSU, which had moved south of the city 2
later in year — Stone & Webster formed the Engineers Public Service Company to control its public utility operating companies through stock ownership ref
November 9 — city allowed BRECO to East Blvd Line with buses 1
early in year — North Baton Rouge Line replaced by 5 buses 1
August 26 — Public Utility Holding Company Act of 1935 passed to regulate electric utility holding companies, effective October 1
? — Stone & Webster "opted to divest itself of its utility holdings" ref
April 23 — City Belt Line ended; only buses in service 1
Things get hazy at this point. Baton Rouge Electric Company was running the city bus system. Its parent company seems to still have been Stone & Webster Engineering Corporation, itself a subsidiary of Stone & Webster. (Interestingly, Stone & Webster was bought by the Shaw Group in 2000.) While Stone & Webster would eventually get out of the picture, they seem to still be in it. What I can't figure out is how the Baton Rouge Bus Company was created.
? — Gulf States Utilities Company merged with BRECO underneath holding company Engineers Public Service Company ref
? — by this year, Engineers Public Service Company controlled the Baton Rouge Bus Company, Inc., but the U.S. Securities and Exchange Commission basically ordered Engineers to divest ref
? — Stone & Webster leave Engineers Public Service Company as the principal holding company ref
Things still hazy. How did stock get sold from Engineers Public Service Company to United Transit Company?
? — Engineers Public Service Company no longer the parent company of Baton Rouge Bus Company; in fact, there is no parent company (uncorroborated) ref
December — United Transit Company of Richmond, VA, owned controlling interest in Baton Rouge Bus Company (uncorroborated) 2
? — United Transit Company bought controlling interest in Baton Rouge Bus Company (uncorroborated) ref
? — under pressure from the SEC, Engineers Public Service dissolves itself; Gulf States Utilities separated to become a free-standing entity (irrelevant to the bus system, but still interesting to know) ref ref
February-June — city-parish council voted to raise fares on the city's buses, leading to a bus boycott ref
It's not clear to me how the council could vote on fares for a private company. But I suppose this did happen before with the streetcars when the city set the rules on what the franchise could charge. Weird.
March — controlling interest in United Transit Company, parent company of Baton Rouge Bus Company, purchased by American Transportation Enterprise (ATE) of New York 2 ref
November 20 — Keith Lanneau purchased all of the stock from ATE; renamed company Metro Transit Corporation (MTC) ref
late July and early August — City of Baton Rouge created Capitol Transportation Corporation (CTC), a non-profit municipal corporate agency, and bought up eight small interurban bus operations ref
August 21 — City of Baton Rouge purchased MTC and consolidated all the various routes ref
May — administrative, maintenance, and transfer facility built at 2250 Florida Boulevard ref
Still working on the recent decades.
One thing I've learned from all of this research is that utility and street railway companies were bought very frequently before 1910. I'm not sure if it's coincidence, but around that time, holding companies got very popular. It was very common for the nation's urban streetcar companies to be owned by a holding company off in some other state. And quite often the streetcar company was very closely tied to an electric utility company. The reason is financial: I don't understand it, but the regulated utility company could sell electricity to the streetcar company in an unregulated way, somehow ripping off consumers in the process. That's why the Public Utility Holding Company Act of 1935 was created. At that time, streetcar operating companies were dropped left and right and bought up by other private companies to be dismantled. Baton Rouge was just one of many cities affected by all this mess.
As for how the long line of private businesses ended up as a government-run affair, that is also pretty common. By the '60s and '70s, buses just weren't making a profit anymore. People loved their cars and the suburbs were expanding considerably. No bus routes could possibly compete with suburban driving. I guess city governments felt they had to take care of their poorer citizens, so they bought the bus companies. With tax-payer assistance, they were able to hobble along without going out of existence.
Baton Rouge shares a similar history of its transit system with other cities, but I don't know if Baton Rouge now diverges with its current dismal transit funding. From what I've read so far, Baton Rouge is a good bit behind other comparable cities on how to properly fund and design its transit system. Something else I haven't researched: does any city have a private company running its transit system?
The above time line is mostly accurate. I still think there are some short-lived companies that are missing, such as the Baton Rouge Electric Light and Power Company from 1889 or so until some other time. It's pretty hard to keep straight which are the utility companies and which are the transit companies. I'm also missing some sources that could tell me when some companies began, such as the Baton Rouge Bus Company. I just guessed on that one.
Then there are all the rich white guys. I haven't even really gotten into them simply because there are so many of them. They hop around from company to company as owner or president or board member, affecting policy and making decisions that affect everyone else. For example, Benjamin Raphael Mayer could be on the time line from around 1891 until 1900. He was involved with Baton Rouge Electric Light and Power Company, Capital Railway & Lighting Company, and Home Electric Company. He was president for each one at some point. But before all that, he was owner of Baton Rouge & Western Transportation Company. The network must have been small back then because these guys got around.