Beyond the power struggles within the CPSU that allowed Khruschev to consolidate his position, the main reason why he was “allowed” to get away with de-Stalinization is because of his abuse of trust. It’s the same thing with Gorbachev later, really, but especially so during Khruschev’s time. Both Soviet citizens and leftists around the world trusted the USSR in the 1950s. They recognized the heroic struggle and undeniable contribution of the USSR and its people in the war against fascism. They saw the blatant persecution and censorship against the left in the Western world following the ousting of Wallace in the 1944 Democratic convention and Truman’s coup as FDR’s successor. They trusted the CPSU to do the right thing.

There were, in essence, two camps in the left before the 20th CPSU Congress: those that had grievances with Stalin and initially saw some criticism of Stalin as not necessarily unwelcome until they later realized over time how far Khrushchev took it and the fallout; those that deeply admired Stalin and thus transitively trusted the CPSU which he led and built, meaning that when the CPSU under Khrushchev turned against Stalin himself, the latter group was completely paralyzed and didn’t know how to respond.

Many leading parties in the Comintern belonged to the first camp. Stalin completely alienated the Yugoslavs through his overreaction to Tito’s attempt at market socialism. The Communist Parties that fell into the Western NATO sphere of influence felt betrayed, especially Italy’s CPI and Greece’s KKE, over his abandonment of them through Stalin’s fears of provoking a WWIII. Stalin may have been right and the USSR deserved peace, but being right had its consequences as well for the Italians who he advised to hand over their arms to the soon-to-be NATO regime and his feuding with Tito which allowed the reactionaries to defeat the KKE in the Greek Civil War. Churchill claimed that he settled the division of Europe and the surrender of Greece with Stalin through a simple five minute chat and officiated with a napkin agreement.

The CPC themselves initially did not denounce Khrushchev because Stalin deeply let down the party through his advice in the 1920s of demanding the CPC to subordinate themselves to the KMT, which led to the 1927 massacre and purge by the fascist Chiang once he took over the KMT. Stalin also deeply distrusted the CPC following 1949 and thought they were a nationalist force and a “fake revolution,” a denial of socialist comradery which was deeply insulting to all the CPC’s heroic first generation like Mao, Zhou Enlai and Deng that fought off the Japanese and liberated China from the KMT. To his credit, Stalin was a man of principled integrity and when he was proven wrong after seeing the Chinese People’s Volunteers rescue the DPRK, he completely corrected course and apparently never again disagreed with Mao on the handling of the Korean War again, even to the point of always siding with Mao against Kim Il-Sung.

Also importantly, like Caligula in the Julian-Claudian dynasty of imperial Rome, Khruschev’s early years were seen as a “honeymoon” period. The SED in the DDR also chafed under Stalin because while they understood and agreed with the necessity and righteousness of German reparations to the USSR, the fracture of Germany meant that the DDR was forced to foot the entire reparations bill. The USSR absolutely deserved reparations but this forced the DDR into a catastrophic lose-lose “catch-22.” As the least developed region of the old Germany and only half the size of the BRD, the DDR was already in an imbalance with the Wessis. With the US sponsoring the Marshall Plan (which contemporaries largely only saw for its "benevolent" face value and failed to see as the self-serving financial imperialism it really was), the reparations to the USSR meant that the DDR-BRD economic dichotomy went from the DDR stagnating-BRD improving to DDR worsening-BRD improving. This later led to the material disparity and population flight that then forced the SED to construct the Berlin Wall. Khruschev annulled the reparations and this was widely appreciated in the DDR. With the CPC, he further extended Soviet aid to China meaning that his early years were the height of the Sino-Soviet alliance and this furthered the CPC’s hesitation at instantly denouncing Khrushchev.

This was the camp in the left that initially tolerated the criticism of Stalin. The other camp, those that trusted Stalin and the CPSU, were for the most part too completely stunned, when the latter turned on the former, to denounce Khrushchev. At "best," this led to simply rejection of Stalin and a swerve towards following Khrushchev. At worst, this led to complete disillusionment with the entire socialist cause. How this occurred is best exemplied from the story of Eva Kaufmann, a SED party member, and her reaction to the 20th Congress as a youth in the FDJ, the Communist youth organization in the DDR.

"People who thought like me had no doubts that the new order was a good thing, so when I heard from a friend who wrote to me from West Germany that there were camps in the Soviet Union and people were being murdered, I said to myself, “That’s propaganda, it’s simply lies.” Then when the Twentieth Party Congress of the CPSU revealed the atrocities, it was a terrible shock, even through the reports about the terrible number of victims were not very clear. We were allowed to listen to Khruschev’s secret speech which was read out to us and it was clear to me that what was now being revealed would mean a very deep crisis for the whole communist movement for the socialist countries."

The Twentieth Congress abused the trust of people in the institution of the CPSU to then destroy their trust in Stalin. As a consequence, they felt betrayed not only by Stalin but also the CPSU which had “hidden” his actions prior to the revelations. This had immense consequences through its inescapable logical conclusion: if even Stalin, who led the USSR to become the principal force that defeated fascism and liberated Eastern Europe, did all these things, then all future socialist leaders could also have the potential to turn out to be “criminals.” No one could trust the motives of any socialist leadership if they accepted the narrative of the 20th Congress that Khruschev put out, since Stalin “got away with it” during his own time and it was only through the voluntary disclosure of his successor that allowed “the truth to come to light.” This led to a damnation of any socialist leadership that was unfalsifiable and the sustained rise of the chauvinistic and smug Euro-“Communism."

As Kaufmann’s story also showed, Khruschev’s betrayal also legitimized anticommunist Western propaganda. Leftists were used to the propaganda barrage against the socialist cause and against the USSR and had generally learned to dismiss it. Because the most openly anticommunist regime was the fascist reich, the revelation of its own atrocities after WWII thus transitively debunked all anticommunist and anti-USSR narratives as propaganda in the eyes of most leftists. As Kaufmann shows, this allowed a cognitive dismissal of all subsequent anticommunist propaganda as the Cold War began. For the CPSU to reveal that not only did Stalin do wrong things but criminal things beyond even what Western propaganda alleged then legitimized anticommunist sources of information from the West. This led to blowback against the USSR and led to the schism between Khruschev himself and Western leftism after the 1956 intervention in Hungary because Western leftists felt compelled to question Khruschev’s rationale and bought the shrill Western narratives that the Hungarian reactionaries were mere “reformers.”

In the socialist world itself, many people were utterly disillusioned and lost their trust in authorities entirely. Nearly all the dissidents, reactionaries and soc-dem “reformers” that came out of the woodwork in the Gorbachev era, reading through their writings, directly attribute trace their own disillusionment with the socialist system through the common origin story of their shock at the “revelations” of the 20th Congress. Some people like Keeran and Kenny in “Socialism Betrayed” see Khruschev’s later, more “evenhanded” comment that "All of us taken together aren’t worth Stalin’s shit” (the truest thing he ever said) as a sign of desperate damage control, but it was far too late. A CPSU leadership collectively worth less than Stalin’s shit had turned the image of Stalin, the CPSU and socialism itself to shit. Later, the anti-Stalin agenda was used in the Gorbachev period as a powerful propaganda cudgel for the reactionaries to resmirch and sideline Marxist-Leninists, as can be seen from the ouster of Ligachev following his promotion of the letter by Leningrad chemist Nina Andreevya who defended Stalin. The Overton window had moved so far to the right in the USSR that this defence of Stalin was able to be used to purge Marxist-Leninists from leading government positions, directly causing the counter revolution that led to the collapse of the USSR.