One of the many reasons not to do this was that the US would oppose it strongly. It saw the Free Officers as pro-Western (which was not necessarily wrong at the time):
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"Washington was well aware that many Arab regimes were quite unstable in the early 1950s. In Egypt, a dissolute king, quarreling politicians, extreme poverty beside a complacent elite, popular dissatisfaction, and growing extremist leftist and Islamic groups combined in a volatile mix. "Talk of a coup d'etat is in the air," wrote U.S. Ambassador Jefferson Caffery in November 1950. The West's prime security interest in Egypt was preserving the sprawling British Suez Canal base for use in time of war or crisis. Secretary of State Dean Acheson urged Anglo-Egyptian cooperation rather than confrontation. Egypt, stung by past British interference in internal affairs, preferred the departure of British troops and the transfer of the base to its own control. When Cairo abrogated the Anglo-Egyptian treaty in October 1951, Washington supported Britain but urged the British to accept a compromise solution.
"Acheson was appalled at Prime Minister Winston Churchill's preference for military responses. When massive riots broke out in Cairo in January 1952, Washington refused Churchill's request for U.S. forces to help squelch the unrest. Acheson replied that the base could not be maintained against the Egyptians' wishes. To solve the impasse, the United States suggested the creation of the Middle East Defense Organization (MEDO), designed to integrate Egypt and the Suez base into a collective security pact. A "Northern Tier" pact was a fallback option. Failure to resolve the Anglo-Egyptian stalemate, warned Assistant Secretary of State Henry Byroade in July 1952, "would lead to riots and disorders which the Egyptian authorities might not be able to control." American influence, he urged, must help produce a compromise. Just forty-eight hours later, Nasser's Free Officers overthrew Egypt's monarchy.
"The United States had some knowledge of but little involvement with the coup. The CIA's Kermit Roosevelt visited Cairo shortly after the January riots, and U.S. officials still hoped that a strong prime minister might take matters in hand. In late March, however, Roosevelt learned of the planned revolution and of Nasser's role as leader of the Free Officers, a group that the U.S. embassy had considered a purely reformist organization concerned only with military affairs. A few hours after the takeover, Major Ali Sabry, one of the plotters, contacted his friend Lieutenant Colonel David Evans, a U.S. military attache, with a message from the new revolutionary council. Its sentiments were pro-Western, Sabry announced, and he requested that the Americans block any British intervention. When King Farouk personally called the American and British embassies to request help, both refused. The revolution had triumphed.. .
"In his first evaluation of the new regime, Ambassador Caffery considered the Free Officers to be an amorphous group without any program, "bound together by common disgust with their superiors." Their figurehead leader, the popular General Muhammad Naguib, was not "a particularly strong or intelligent leader."' Nevertheless, the officers seemed friendly to the United States and expressed a desire to take part in the Middle East's defense. Britain quickly offered military aid in exchange for settling the base issue. Caffery was generally optimistic: the United States should not rush Egypt toward an acceptance of MEDO, he suggested, but it should help Cairo build an effective and inexpensive military force for protecting the country.
"As predicted, the new Egyptian government began to court the United States. .."
Barry Rubin, "America and the Egyptian Revolution, 1950-1957,"
Political Science Quarterly, Vol. 97, No. 1 (Spring, 1982), pp. 73-90
http://www.jstor.org/stable/2149315
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As I wrote here some time ago, "If the monarchy was unpopular and would be made even more so by British intervention to save it from immediate overthrow, it certainly seemed better to acquiesce in the Free Officers coming to power than to let the opposition to the monarchy find its outlets in the Communists or the Muslim Brotherhood."
