This is a very complex question that's actually asking about many different, overlapping issues. Firstly, I'd start by suggesting that the question itself presupposes a form of US primacy in the Cold War that in itself is a form of exceptionalism. What we refer to as 'the Cold War' was always multipolar and not simply bipolar (in the sense of being about the USA-USSR confrontation). From the 40s to the mid-1950s, the British empire is certainly a third pole. Likewise the People's Republic of China after the Sino-Soviet Split that eventuated from the mid 1950s onwards. I'd also challenge the term 'proxy wars'. That's something that historians try not to use any more, as saying something is a 'proxy' war elides the local agency and perhaps obscures the local and regional contingencies of conflicts such as Korea, Vietnam, Angola, etc.

Secondly, it's also important to point out that - as Daniel Sargent persuasively points out in his book A Superpower Transformed (and he's far from the only scholar to make this case) - in the mid-1970s there was a significant number of observers who thought that the Cold War was over. Indeed, Jimmy Carter was referred to on multiple occasions as America's 'first post-Cold War president'. For another perspective, the historian Anders Stephanson contends that the Cold War was on one hand a distinctively American project and that the Cold War was effectively over in 1963 when US hegemony and Soviet decline was effectively assured (I don't agree with Stephanson, but his argument is certainly worth engaging with).

Thirdly, there's the vital point that we sometimes overstate opposition to US intervention abroad within a domestic context. Right up to the Vietnam War's denoument there remained a huge proportion of the US electorate who supported the conflict and the US global stance more generally. Connected to this, we can look back and go "Nixon was obviously a crook!" but that again obscures the fact that he was hugely popular and won the 1972 election by a gigantic margin (for various complex reasons it's not possible to go into here). When we talk about 'Americans', who are we talking about? Because we're discussing a complex polity made up of millions upon millions of people, so it's simply not possible to say "Americans thought this..." in anything but the most general (and useless) terms.

That's all kind of prefatory to the rest of this answer. When the US withdrew from Vietnam in 1973, the 'Cold War' geopolitical space was dominated by the idea of detente - the thaw in relations between the US and USSR, the US and PRC, and Western and Eastern Europe. 'European detente' is sometimes the forgotten factor here. As Jussi Hanihmaki notes, the twin crises of Berlin and Cuba reminded Europeans just how vulnerable they were to the excesses of the Cold War. The thawing of European tensions emerged out of a challenge to the dangers posed by Cold War bipolarity.

Detente did manage to reduce tensions and lead to genuine diplomatic achievements. But then it collapsed and the Cold War was 'on' again. Why? Detente had in large part been driven by US aims and ambitions, and it was American domestic opposition that contributed in large part to its collapse. Despite achievements such as the Strategic Arms Limitation Treaty (SALT), detente was often more perception than reality, and was challenged by superpower actions and internal opponents.

During the Nixon years and from 1974 when Gerald Ford took office in the aftermath of Watergate, many Democratic congressmen charged the Republican administration with leaving the USA in a militarily weaker position. The 1975 Helsinki Accords were also criticized. Opponents argued that they accepted the ongoing Soviet domination of Eastern Europe. Moreover, Nixon and Ford’s unwillingness to criticise the USSR’s human rights record – recalling that human rights were a cornerstone of Helsinki – came under fire. International figures such as the famed Soviet writer and dissident Alexandr Solzhenitsyn attacked Helsinki as a “betrayal of Eastern Europe.”

The perception gap between what détente meant in theory and what actually eventuated was apparent in the Middle East and Africa. For example, when the US involved itself in the Middle East, this implied to the USSR that détente did not mean a reduction in efforts to support developing world or non-aligned nations.

So why did détente ultimately collapse? Olav Njolstad usefully and succinctly identifies five key factors:

1: Underpinning détente was a basic lack of mutual trust.

2: There was a lack of shared values and visions. Nuclear restraint aside, the two sides held vastly differing political ideals and nurtured different hopes for the future of world affairs.

3: Thirdly, there was no real economic interdependence between the USSR and the West. The sluggish, weak, outdated Soviet economy had little to offer capitalism.

4: There was also a mutual lack of restraint that stemmed from the zero-sum game of Cold War geopolitics. Both superpowers still sought geopolitical advantage at the expense of the other.

5: Finally, there was the arms race. On both sides there were multiple forces putting pressure on moves to restrain the arms race, for and against. And such was the extent, diversity, and complexity of the nuclear complex, it was impossible to judge the situation objectively.

In the end, the reason for the Cold War's continuation is historically explicable and to centre the United States overmuch obscures a lot of important things. Anyway, this is kind of a brief answer, so if you have any follow-up questions I'll try to clarify points.

Malcolm

Sources

Hanhimaki, Jussi, 'Detente in Europe, 1962-1975', in Melvyn P. Leffler and Odd Arne Westad, The Cambridge History of the Cold War, Vol.3 (Cambridge: Cambridge University Press, 2010)

Njolstad, Olav, 'The Collapse of Superpower Detente, 1975-1980' in Melvyn P. Leffler and Odd Arne Westad, The Cambridge History of the Cold War, Vol.3 (Cambridge: Cambridge University Press, 2010)

Sargent, Daniel, A Superpower Transformed: The Remaking of American Foreign Relations in the 1970s (Oxford: Oxford University Press, 2015)

Stephanson, Anders, 'Cold War Degree Zero', in Joel Isaac and Duncan Bell (eds.) Uncertain Empire: American History and the Idea of the Cold War (New York: Oxford University Press, 2012)