Well after WW II Berlin was off limits to any Non-Allied planes. There were only three "corridors" to access Berlin and Berlin was not a capital. West Berlin wasn't and for years the Western allies ignored the East.

Frankfurt was the main USAF base for goods into Berlin, transfers to the middle east and troops.

Also Frankfurt had been considered as the capital after the war, but due to manipulating the Agenda - Bonn on.

Hamburg is too far north to be practical.
Munich to far south - and not very industrialized ...
Also Bavaria is not a full member of the Germany in a weird way -- they never ratified the constitution -but declared to accept it - like this they are a Freistaat.

Cologne was too destroyed after the war and then the Airport was not under US control but the Brits . So what was left was FRA