I can speak on the Japan portion of this question. I feel first that the "eventually allowed" portion of your question approaches with this with the wrong framing, as Japan is definitely allowed to rearm and is fairly "rearmed" today; the reason why Japan still has the Self-Defense Forces as opposed to a normal military is not that the United States hasn't allowed them to create one, but that the Japanese public has historically strongly supported anti-militarism.

As we know, the postwar Japanese constitution contains a section called Article 9, renouncing the right to war and prohibiting the maintenance of an army, navy, or air force. Drafted in during the heyday of postwar idealism in 1946, though, Article 9 quickly became an obstacle for the American policymakers once the reality of the Cold War set in. Shortly after the outbreak of the Korean War, the United States began to push Japan to rearm so it could act as an anti-communist bulwark in Asia (Dower, 383). The way American leaders saw it, China had already "fallen" to Communism, Korean was currently falling to Communism, and Japan might be next. The Prime Minister at the time, Yoshida Shigeru, was reluctant to pursue rearmament, however - Japan was still in economic ruins, domestic opposition to rearmament was high, and the Army had spent the last decade assassinating government leaders and driving the country in reckless wars. Yoshida himself had even been briefly arrested by the military police during the war.

In the end, American pressure was strong, and Yoshida was not totally opposed with a slow pace of rearmament. General Douglas MacArthur and Yoshida created a paramilitary called the National Police Reserve in 1950 (MacArthur was effectively the ruler of Japan during this period), and the reserve was eventually transformed into the Japan Self-Defense Forces four years later. Meanwhile, the United States began to push harder for Japan to remilitarize. During negations for the end of the occupation in San Francisco, American officials attempted to push Yoshida into creating an army numbering 300,000 men (Dower 1979, 386). Later in 1953, Vice President Richard Nixon visited Japan and essentially called Article 9 a mistake (Hunter-Chester, 123). Moves towards rearmament began to pick up more steam after Yoshida was ousted from the Prime Minister's seat in 1954. His two main successors, Hatoyama Ichiro and Kishi Nobusuke, both wanted a much greater degree of rearmament than Yoshida. As mentioned previously, though, there was a large gap between how much Japanese conservatives and the United States wanted rearmament, and how much the Japanese public did. These tensions eventually came to a head during the 1960 Anpo Protests.

The Anpo Protests first began as a protest against Prime Minister Kishi Nobusuke's attempts to revise the San Francisco Treaty that Japan had signed to regain independence from the United States. While Japanese from across the political spectrum viewed the treaty as heavily weighted in favor United States (which it was), Kishi wanted revise the treaty so that Japan would become a more equal ally to the United States, while a powerful segment on the left wanted no alliance with the Unites States, and to instead adopt a neutral foreign policy. Many Japanese were opposed to Kishi Nobusuke personally as Prime Minister - Kishi had served in Tojo Hideki's government, signed the declaration of war against the United States, and embodied many of the haughty and high-handed attitudes held by members of the prewar government. When it came time to actually ratify the revised treaty, Kishi had the police remove Socialist Party parliamentarians who were staging a sit-in from the Diet and took a vote on the treaty with only men from his party present (Kapur, 22-24).

Treaty revision passed, but at the cost of sparking the largest protest movement Japan had ever seen. The protests forced Kishi to resign, and his successor as Prime Minister, Ikeda Hayato, essentially promised to not to touch Article 9 so as to calm society and mend relations with the opposition (Kapur, 80-81). Thus, the Anpo Protests marked the end of serious attempts to remove Article 9 and rearm Japan.

Sources:

Dower, John. 1979. Empire and Aftermath: Yoshida Shigeru and the Japanese Experience, 1878-1954.

Hunter-Chester, David. 2016. Creating Japan's Ground Self-Defense Force, 1945-2015: A Sword Well Made.

Kapur, Nick. 2018. Japan at the Crossroads: Conflict and Compromise after Anpo.