US backs down over the cuban missile crisis

With regard to people saying Khrushchev would stay in power, this is very questionable. Ian D. Thatcher lists the reasons Khrushchev's successors gave for his ouster:

"The anti-Khrushchev charges included policy failures, domestic and foreign. At home industry and agriculture were under-performing. Abroad relations had soured with China. Most importantly, these policy failings were linked to Khrushchev's misdemeanours as leader. Khrushchev, it was claimed, was bypassing the Presidium and the Central Committee. He had taken to issuing decrees in the name of the Central Committee that were in fact on his own initiative. Khrushchev had surrounded himself with sycophants and family members that formed his inner-staff. Presidium colleagues could not reach him directly but had to deal with this entourage. Khrushchev simply ignored the advice of the Politburo, assigning key duties to his private circle outside the control of the party elite. In this sense Khrushchev broke party norms and even engaged in corruption. The award of honours to his son and son-in-law was noted, as well as the use of state money to fund family excursions abroad on what was supposed to be official business.

"Such irregularities, it was said, occurred because Khrushchev had concentrated power in his own hands. Moreover, he did not know how to use this power sensibly. While having little or no expertise, he considered himself an expert in agriculture, diplomacy, science, and art, and his interfering had devastating consequences. Khrushchev defended the quack geneticist Lysenko, for example, despite warnings from eminent scientists. Khrushchev was unable to control his thoughts and most importantly his mouth. He had upset prominent friends within the socialist camp, causing trouble in relations with China, Albania, Romania, and Poland. Khrushchev would make promises to foreign heads of state for which he had not received the required authority from the Presidium or Central Committee. In the USSR Khrushchev had engaged in constant reorganisations of economic and party bodies that brought only additional confusion and threatened to split the party. Yet, paradoxically, this sad story of failure and illegality was accompanied by excessive praise of Khrushchev in the media. Ignored and often insulted by the man who had turned meetings of the Presidium into 'empty formality', Khrushchev's colleagues had to act. Khrushchev's 'petty tyranny' unlike Stalin's was not based on terror, but this did not excuse it. If anything, it was 'harder to struggle with a living cult than with a dead one. If Stalin destroyed people physically, Khrushchev destroyed them morally'.

"This indictment against Khrushchev was a clever use of his own denunciation of the 'cult of personality' against Stalin. (It also borrowed from the criticism, made by Stalin much earlier, that Khrushchev was guilty of 'hare-brained' schemes!) Khrushchev now found himself portrayed as a leader out of touch with reality, as making a mess of policy, and as flouting party rules, ignoring and belittling comrades, whilst surviving in an artificial bubble of excessive praise from official propaganda and an inner coterie of toadies..." https://history-groby.weebly.com/uploads/2/9/5/6/29562653/khruschev_and_stalin_1.pdf

Thatcher feels that this indictment is largely unfair, but it is the one that Khrushchev's successors made in justifying his ouster, and note that the Cuban Missile Crisis is not even mentioned (at least explicitly)!
 
Could a mindset like in the book 'The Gladiator' by Harry Turtledove arise? Something like 'The US, the heartland of capitalism itself, is not ready to fight communism and defend its outdated ideology. They don't belive themselves anymore'. This would greatly bolster communist popularity in the west.

You'd need to establish a steady pattern of concessions to make such a mindset stick, and given any administration that backs down on a major point would see it's popularity tank and the other party naturally move to capitalize on the opening that won't be happening. That's one advantage of the unsteady forgein policy the "scheduled coup attempt/revolution" that occurs every four years has: you're not doomed to get stuck in a rut
 
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