The United States to this day has military basing in Germany, Italy, Japan, etc. What was the thinking during that time not to warrant "taking" real estate in Tunisia, Egypt, etc?
The answer is that they did have bases in North Africa. Wheelus Air Base in Libya was a major training facility in the early Cold War. Morocco had a network of SAC airfields at Sidi Slimane, Ben Guerir, and Nouasseur. As to why these bases never became permanent like Kadena is really a result of two separate trends. Firstly, the political changes that resulted from decolonization made the issue of a foreign military presence politically unpalatable for many leaders of the first decolonized generation. While the permanent base structures in Germany, Italy, and Japan have created friction between the US and the host country, their existence did not question the fundamental principles of the state. A strong foreign military presence on newly independent soil was both a symbolic and potential threat to national sovereignty. The second overarching reason is more pragmatic as US military needs shifted away from needing a vast network of subsidiary air fields and forward bases during the mid-Cold War. Many of these bases were already understaffed and the budgetary and manpower pressures of Cold War and the expansion of US tanker assets meant that these affiliate bases lost their strategic raison d'être.
As a matter of fact, the United States had several bases in North Africa after World War II and the largest, Wheelus Field, was expanded as a training facility. Over 4,000 American troops were based at Wheelus. SAC staged bombers from Wheelus, while the Libyan desert was used for live-fire missile and gunnery exercises.
In the 1960s, Wheelus' mission changed as SAC moved from bombers to missiles; its training function expanded, and it also opened its gates to the large American expatriate community working in Libya's oil industry, allowing U.S. citizens to send their children to school on the base. Still, with the Vietnam War consuming military budgets, Wheelus was no longer a viable investment and the U.S. and Libya agreed to close the base in 1970.
A few months before this happened, Colonel Qaddafi seized control of Libya - the turnover occurred on schedule, and Qaddafi also nationalized the oil industry. The airfield was renamed and made the headquarters of Libya's air force. The US Air Force returned to Wheelus to bomb it in 1986, along with other targets across Libya.