In general, you have people who assume nuclear deterrence was a very important and real force that is largely responsible for the lack of superpower conflict. There is very little that tries to "prove" this in any real sense though; it's hard to know what you'd look for (a memo that says, "if we invade X, we'll get nuked, so let's not do that!" — such things don't generally pop up). Most of these people take it for granted as obvious. Most scholars are probably in this category, but that's because it's sort of the default position (and usually the unexamined assumption).

You can also find people who would say that fears of retaliation or escalation are definitely present along with many other non-nuclear reasons (economics, international opinion, domestic pressures, emotional associations, etc.) for not doing these things. Maybe we could call this the "mixed" case — people who are a bit more concerned with the fact that the history of nations is pretty complicated when you drill down into it.

Finally, there are some who deny that nuclear deterrence is "real" — that it's basically an idea that some think-tankers cooked up and has very little to do with how leaders act or think. They would point out that, for example, the US did not really have a classical deterrence-based philosophy for much of the Cold War (it leaned very heavily into the idea of first strike, which is not deterrence, and was very uncomfortable with mutual vulnerability ideas), that even in the absence of straightforward nuclear deterrence scenarios countries avoided using nuclear weapons (e.g., the reason for US non-use of nukes in the Korea War was not because of deterrence, because there was really no credible threat for reply in kind; the Soviet non-use of nukes in Afghanistan, as an another example, is one in that classical deterrence theory doesn't really explain), and that there is no way to really "prove" that deterrence is real or has some effect. Said people are almost universally associated with arguments for the abolishment of nuclear weapons, and see undermining the idea of deterrence as an important way to make that seem feasible.

It's probably clear where I stand on this — somewhere in the middle of two extremes — based on just my presentation of the ideas alone. I think the "deterrence deniers" have more interesting arguments than the people who take it for granted, but I find it a bit of a stretch to imagine that the presence of nukes and the possibility of retaliation and escalation played no role in discouraging conflict. At the same time, I find it very annoying when people (many associated with promoting nuclear weapons in various ways) make it sound like it was just the presence of nukes that resulted in the shift of the nature of warfare in the late 20th century (away from massive conflicts between major states, and instead a mess of bloody proxy wars), when there are a lot of other additional factors that were leading in that direction as well.

Most politicians, armchair historians, and pundits have never even thought this was a question worth asking — what exactly was the role of nuclear weapons in international politics in the Cold War and beyond? — to be sure, and are just re-amplifying cultural messages that have been spouted since the 1950s at least. There are historians and political scientists who are interested in this question, though.

is it imaginable that the lack of direct, armed conflict between US and USSR was not primarily due to nuclear weapons, but could in fact be attributed to other causes, either fully or partly?

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Political decisions are rarely, if ever, monocausal -- but in the case of nuclear deterrence, the overwhelming fear that direct armed conflict between the superpowers (resp. their alliances) would too easily escalate into nuclear war is almost omnipresent in the political decision making of the cold war, from 1949 to 1990.

Having said that, there is -- and that is what foreign policy/security/diplomatic historians do -- plenty of evidence of individual minor factors that shaped the particulars of decision making in the cold war. Power shifts, squabbles within alliances, other local actors, etc played large roles within the overarching framework of superpower nuclear competition.

There are, though, various phases in the cold war philosophies of what (in terms of strategic game theory) nuclear deterrence actually meant. These can be described in three phases, "Fire at will", "Fire as situation requires", and the final phase, MAD (mutually assured destruction).

The United States, throughout the 1950s, for instance, considered any small incident anywhere as escalatable into one large conflict, and that translated into a (seemingly fairly primitive) logic culminating in Eisenhower's attitude that (I paraphrase) "If the Soviets really want war, they can have it." However, in the second half of the 1950s, military and strategic thinkers increasingly considered that it was not credible to threaten all-out nuclear war if a crisis was clearly perceived as local and limited. This became particularly clear as the Second Berlin Crisis emerged, where Soviet intentions seemed primarily bent not on attacking West Germany but somehow forcing the West into ceding West Berlin. The thought line there was roughly: "If the Soviets do not believe we go to global nuclear war over West Berlin, they might be tempted despite the nuclear deterrent to go for military action. What do we do if the Soviets choose this action (misreading the West's determination), and our own allies (UK, France, West Germany) then hesitate and ask us not to press the button? Then deterrence failed anyway (because it did not preclude the Soviet side to choose to attack), and we have no course of action with a good outcome. So we must make nuclear deterrence work even for cases of smaller theatres of conflict."

This brought about the development of the strategies of flexible response (most forcefully by General Maxwell Taylor in his book "The Uncertain Trumpet") which called for individual escalating deterrence plans for each theatre or situation, to make deterrence credible even for such smaller "chess" moves, precisely to avoid escalating into global thermonuclear war by basically offering individual escalation plans for each crisis leading to the center of the web, global thermonuclear war. Thus, nuclear weapons had left the realm of being simple weapons for use in war, they were meant to become signals in a step-up that you are ready to go to full global use (and it's what I call the "fire as requires" phase, though surely somebody can find a better quip to call it).

One such classic thought piece that showed the change of thinking here was Thomas Schelling's paper "Nuclear Strategy in the Berlin Crisis" (1961), which he had written as part of a secret RAND corporation game theoretical thinking paper for the Pentagon and White House. In it, he said about the tactical use of nuclear weapons in such a limited scenario as West Berlin:

However few the nuclears used, and however selectively they are used, their purpose should not be “tactical” because their consequences will not be tactical. With nuclears, it has become a war of nuclear risks and threats at the highest strategic level. It is a war of nuclear bargaining. ... Targets should be picked with a view to what the Soviet leadership perceives about the character of war and about our intent, not for tactical importance. A target inside the USSR is important because it is inside the USSR, not because of its tactical contribution to the European battlefield. ... Extra targets destroyed by additional weapons are not a local military “bonus”; they are noise that may drown the message. They are a “proposal” that must be responded to. ... If nuclear weapons should be resorted to, particular weapons will be fired from particular locations to particular targets at particular times. Messages may need to accompany the weapons; if so, they must carry particular language. The concept of selective strategic bargaining is not enough, there must be plans [underlined in original] for how to do this.

After the Berlin Crisis, this general strategic concept had pretty much pervaded Western nuclear strategy thinking (1961 Dep. Sec of Defense Harry Rowen once told me in an interview when I showed him the Schelling paper in the 90s: "Oh, that paper. Yeah, it just put into words very eloquently what we all thought."). Soviet documents showed a tendency to a similar philosophy, though they would not use the same exact game theory jargon.