What I have in mind is that if the cold war had then relaxed, we on the U.S. may not have propped up seemingly every dictatorship perceived to be friendly to our interests, nor would the Soviets seemingly followed a policy of rushing in and arming rebel groups. Nor we would on the U.S. view any reduction in super favorably terms to corporate interests to be intolerable 'communism' or 'socialism.' In fact, in a cold war light as it were, just maybe West and East would compete on who could do a better job at genuine economic development in third world countries and winning allies this way.
I suppose I’ll be the one to say it
It doesn’t particularly matter who the President is, or who the General Secretary is. The Cold War was not really a matter of how nice the United States or the USSR were and it wasn’t a tragic misunderstanding of world views. The socialization of economies whether by elections or by revolution was perceived, correctly, by the ruling class of the United States as an existential threat. There is a reason why the elected Allende government in ‘73 was treated much the same way as the Cuban government in ‘59. Or how Guatemala and Iran were treated in ‘53 and‘54 versus American interventions in Bolshevik Russia in 1918 or in Nicaragua in ‘79 - ‘80. Across time and space, across different American presidents and events, we see the exact same tendency. The tendency for European and North American capitalist powers to intervene and destroy real or perceived attempts at socializing/nationalizing the economies of nations - peripheral or otherwise.
If a peace-loving freak hippie replaced Stalin as General Secretary of the Communist Party of the Soviet Union, I don’t think it was do much at all to change the temperament of American leaders towards securing obedient clients and neo-colonial relationships with newly independent colonies and towards the extermination of the Communist Party of Indonesia.
It wasn’t the harshness of Soviet policy that conditioned the American elite to see economic shifts to the left as intolerable communism or socialism, it was the dollar amounts and the loss of cheap labor or lucrative resource extraction. Even if you remove the fact of an actually-existing-socialism and big red boogeyman that haunted (haunts?) the nightmares of American policymakers, we have still consistently seen anti-democratic and violent actions taken against colonial subjects seeking economic self-determination. The loss of profits being siphoned via indigenous compradors outweighs any number of bleeding heart liberal tendencies. The history of American occupations in Latin American prior to the advent of Bolshevism is instructive. It wasn’t for kicks that the Union Minière du Haut-Katanga and the Belgian ruling class practically threw money at Tshombe to secede and destabilize Lumumba’s Congo. It was to secure the copper industry and destroy any attempt to sever the Congo from Belgium’s 'gentle paternal hand.’ And boom, we get thirty two years of Mobutu. I would give more examples but I don’t want to veer into current politics.
The chance of a peaceable Cold War in which both sides compete on a fair and free playing field to win over the hearts and minds of the global population is nil.