Not a historian but an intelligence buff here so I'll do my best. Any corrections are welcome and please correct me if I am wrong about anything.

It has less to do with reasoning and more to do with politics, connections, and being in the right place at the right time.

The right place, at the right time
William Donovan, the head of the Office of Strategic Services was a Lawyer before joining the military an eventually becoming the Coordinator of information in 1941, and then in 1942 when the COI became the OSS, he was carried over as the Head of the OSS.

Allen Dulles was a law graduate of George Washington University, was recruited by the OSS during WWII and became the head of the OSS in Switzerland.

Here's where things were solidified. According to Prelude to Terror: the Rogue CIA, The Legacy of America's Private Intelligence Network By Joseph J. Trento, In between the disbanding of the OSS on September 20, 1945 and the formation of the CIA on September 18, 1947, Allen Dulles ran a private intelligence network out of his office at 44 Wall Street, using some the "Biggest names in the business" as his connection to the world to collect information.

"Dulles did it because he felt he had to. "The Soviets were throwing everything they had at us. The NKVD [later the KGB] were eating us alive, and Washington could not make up it's mind about what to do on intelligence"" Prelude to Terror: the Rogue CIA, The Legacy of America's Private Intelligence Network - Page 1.

Dulles was already recruiting former Nazi's for the fight against communism while the US government was trying to figure out what the should do when it came to Intelligence gathering. Dulles was preparing to go head-to-head with the soviets and he was willing to do almost anything to stop them. He reached out to wall street bankers and lawyers who had done business with the Nazi government during WWII to help the process, their secret ties were no longer dangerous and they suddenly became useful. They recruited these former Nazis because of their mutual hatred for communism and technical brilliance. For instance Wernher von Braun was brought over because of his brilliance with rockets and he helped get us to the moon, a huge boost in moral for the Americans during the cold war. The enemy of my enemy is my friend.

The move was met with some protest from the public. Take for instance this song mocking Wernher von Braun and the politicians who brought his the the US by Tom Lehrer.

Here's the lyrics:
And what is it that put america in the forefront of the nuclear nations? and what is it that will make it possible to spend 20 billion dollars of your money to put some clown on the moon? well, S good old american know-how, that's what. as provided by good old americans like dr. wernher von braun.

Gather round while I sing you of wernher von braun,
A man whose allegiance
Is ruled by expedience.
Call him a nazi, he won't even frown.
"ha, nazi schmazi," says wernher von braun.

Don't say that he's hypocritical,
Say rather that he's apolitical.

"once the rockets are up, who cares where they come down?
That's not my department," says wernher von braun.

Some have harsh words for this man of renown,
But some think our attitude
Should be one of gratitude,
Like the widows and cripples in old london town
Who owe their large pensions to wernher von braun.

You too may be a big hero,
Once you've learned to count backwards to zero.
"in german oder english I know how to count down,
Und I'm learning chinese," says wernher von braun.

According to Enemies: A History of the FBI by Tim Weiner, J. Edgar Hoover had already tried to have a worldwide intelligence network and failed. He created the FBI's Special Intelligence Service on July 1st 1940 and sent it's agents mainly to South America. They ran the SIS out of a front in Room 4332 at Rockefeller Plaza in New York City as the Importers and Exporters Service Company. They went abroad under the covers of reporters for Newsweek with the help of the magazine's boss Vincent Astor. The also posed as Stockbrokers for Merrill Lynch, executives of the United Front Company, the Armour Meat Company, American telephone and Telegraph, and US Steel.

The SIS failed badly. Using a false passport Foxworth went to fourteen countries where the SIS was trying to gather intelligence. When he reported back to hoover he stated that the agents had know idea what they were supposed to do or how to do it. Things eventually got so bad that Hoover, sensing the political fallout tried to get the Attorney General to hand over the SIS to the Army or Navy on March 15, 1941.

Politics
Aside from the failings of the SIS there was another reason Hoover never got the job as the director of a worldwide intelligence agency. He was always going to far. He did lots of things that were horrifying and illegal. Under FDR he was allowed to bug and wiretap without warrants anybody he thought was a foreign agent or who he though was subverting the power of the US, including FDR's political enemies. He kept lists of Americans he thought should be locked up in the event of war, based on information he gather illegally. They were not just the head of the Communist party USA (CPUSA) but people who had ever gone to a CPUSA rally out of sheer curiosity.

This let to multiple government officials saying (or being worried) that his organization would be an american gestapo.

With the failure of the SIS and the forethought of Dulles to already begin the fight against communism it was the proposed CIA who won out. The CIA was formed on September 18th, 1947.

The first two Directors of the CIA were military men who didn't really want the job and it showed

Roscoe H. Hillenkoetter, December 8th, 1947 to 1950: The First Director of the CIA was Roscoe H. Hillenkoetter. Truman had convinced him to run the very temporary precurser to the CIA called the Central Intelligence Group. He was carried over to the CIA but he failed to predict the first soviet nuclear bomb test and the invasion of South Korea by the North. He was fired by this and replaced by...

Walter Bedell Smith, October 7th, 1950 to February 9th 1953: Despite major changes smith made at the CIA. Including merging the Office of Policy Coordination and the Office of Special Operations into one division, he didn't really produce any usable intelligence during the Korean war, and he failed to predict the Chinese intervention. He retired from the CIA in 1953 and became Under Secretary of State.

Dulles Forward (February 26, 1953, and Onward)
Dulles was the first civilian director of the CIA and the first one that had what could really be called a passion for espionage. In between his career at the OSS and his career at the CIA he had helped write the Dulles–Jackson–Correa Report criticizing the CIA's thus far. It was partly due to the report that Hillenkoetter had been removed and Smith had been appointed to head the CIA. Because of this, Smith made him Deputy Director for Plans (Covert operations). Less than a year later he promoted him to Deputy Director of Central Intelligence, second in command at the CIA.

Dulles had been head of the OSS in Switzerland and had a zeal for actual covert operations. During his reign he actually did things. They executed a coups in both Iran and Guatemala, due to fears of soviet takeover. The CIA also executed the bay of Pigs invasion, which failed spectacularly.

He was criticized though, because the people the coups put into power were corrupt and violent. Mohammad Reza Shah Pahlavi, who was installed in the coup in Iran used his secret police, the SAVAK, to crush political dissention. This was part of what led to the Iranian Revolution.

Due to these factors and the extreme embarrassment of the BOP invasion, he was forced to resign. However, his career really did set a tone moving forward at the CIA. Military men did not have a great history at the CIA before and they didn't going forward either. Only three Military men have served as the head of the CIA since Dulles.

William Raborn April 28, 1965 to June 30, 1966: Raborn was a Vice Admiral in the Navy who had helped develop the Polaris Missile System and finished it three years early. Johnson appointed him head of the CIA but he didn't really do anything because he didn't know how, as his career had no intelligence experience up to that point.

Stansfield Turner March 9, 1977 to January 20, 1981: Turner was a Navy Admiral who was not popular with the CIA's Human Intelligence (HUMINT) employees at all. He focused heavily on Signals Intelligence (SIGINT) and Technical Intelligence (TECHINT) and neglected HUMINT in favor of these collection methods. He fired hundreds of personnel, and also testified before congress about MKULTRA. He was not a popular director.

David Petraeus, September 6, 2011 – November 9, 2012: Petraeus was more secretive that the director he replaced and was know by some to be harsh to people if they gave him information he didn't consider to be complete enough. His roll as director during the 2012 Benghazi embassy attack has tainted his legacy at the agency. He was not forthcoming with information and critics say that the CIA did not act fast enough and that they were not forthcoming with, or did not know what was happening on the ground.

Since then they have stuck to career Intelligence officers or politicians.