Losing conventional parity means that the USSR no longer has the ability to export revolution or conduct major foreign interventions lest it be confronted by the US/NATO. This doesn't seem like a big problem but it does create a political weakness for whichever officials are espousing this viewpoint. The Soviet military-industrial complex is a deep-seated faction and will not give up their influence and privileges without a struggle. IOTL Gorbachev marketed his reform program (at least in the beginning) on the grounds that economic efficiency was needed to maintain military parity with the West.
Khrushchev wanted exactly what the OP suggests. It was a pipe dream but not at all for some of the reasons you give here--though I certainly grant the Soviet military-industrial complex
was a major factor. And it is conceivable though hardly plainly evident that the Kremlin included some people who dreamed that maybe someday they might be able to "export revolution or conduct major foreign interventions." Perhaps you refer to the latter, interventions, in the context of
internal to the Warsaw Pact. They most certainly did that, repeatedly. But outside the boundaries set by the extent of Red Army advances in the course of defeating Hitler and Japan in World War II, as allies of the western powers and not opponents (yet--obviously people in both the Soviet Union and the West looked beyond the war during the war and the alliance was tense and ambiguous for that reason) the USSR was never once, to my knowledge, able to "export revolution or conduct major foreign interventions." Western powers could and did do precisely that--the coups putting more right-wing and amenable to US interests (as defined by factions like the Dulles brothers, if not our broadest and most humane self-image) in places like Guatemala and Iran, the anti-Nicaraguan Contras of the 1980s, the overthrow of Allende in Chile, these are cases of "exporting revolution and conducting major foreign interventions." The Suez Crisis of 1956 was an example of Western powers, Britain and France in collaboration with Israel, believing they would be able to get away with doing that, and other interventions by Britain and France in their former colonial spheres count as such too. Western powers could do it, but the Cold War was not quite as mirror-image symmetrical as people might assume. The Soviets never had an opportunity to do anything similar--to use brute force based outside the target nation to batter and break its legitimate government and invade to compel a regime change to their liking. Even in Afghanistan right on their border, they only acted with military force after a homegrown domestic Communist coup had taken over on its own, and then factions within it in the course of infighting that threatened to collapse the whole thing begged for Soviet help. In that case the Red Army was able to move in en masse, because of Afghanistan being right there on their border. All other instances of Soviet aid overseas involved much smaller numbers of Soviet troops, and were mostly matters of shipping them arms to be wielded by domestic forces, because the Warsaw Pact did not dominate world trade channels--the western powers did.
There was generally no way that the western powers could legitimately block shipments of Soviet weapons, or even personnel, from going to ports where the government already in power there wanted to receive them. That would, short of declared war, be piracy, and the one counterexample I can think of, the Cuban missile crisis, in which Kennedy implemented a "blockade" of Cuba was precisely a matter of verging on total thermonuclear war. Vice versa there was no way the Soviet navy could mount an expedition to invade and intervene in any country--even nations on the Soviet border were protected by international norms and the readiness of Western powers to threaten nuclear war over any sort of overt invasion.
If anyone in the Kremlin even considered that keeping the Red Army around on the scale they did had to do with readiness to export revolution and intervene overseas, they were dreaming rosy-red daydreams and presumably on drugs of some kind, or at best, looking forward with longing to that equally vague and rosy-red far future in which by "inevitable" processes due to the presumed weaknesses of capitalism and the presumed superior economic and technical prospects of communistic centrally planned economies, the Soviet bloc would gradually gain prestige and legitimacy while the Western bloc would decay and implode; this might open up the prospect of Soviet bloc forces acting as Western powers of the early Cold War years commonly did. But note it would only do so at a time when violent overthrow by external power would be less and less necessary.
Whatever perception you might have that advances of Soviet power into places like Cuba, Vietnam or Nicaragua had anything to do with the Red Army's ability to act like US Marines or British Commandos, I think you'll find no historic evidence to back it up. When the Soviets were described as "intervening" in places like these or Ethiopia or anywhere else that claimed a more or less Leninist inspiration, they were always using legitimate global trading channels to provide aid to domestic revolutionaries who had already secured the beachhead Soviet freighters brought them more guns with, and these domestic rebels were in charge of the success or failure of their movements. It was often the case that the scattered leftist-nationalist movements claiming Soviet support were acting against the interests of the Kremlin, and they got backing because the prestige of the USSR as motherland of Communist revolution would be discredited if they did not support these loose cannon rebels.
So--arguably Soviet arms, which were a major part though not the whole of the large military expenses the OP wishes to discuss saving by means of reliance on ICBM deterrence alone, would be an expense related to "projection of power," but definitely not in the manner you suggest. In a future as envisioned by Khrushchev in which the legitimacy of capitalist regimes is imploding and Leninist revolution is on the march domestically and spontaneously, because of the superior example of the Soviet system, they would hardly require intervention forces, though perhaps circumstances might call for one to be developed.
But where the Soviet Union really really did require massive armies heavily armed was in the matter of keeping control within their own "house"--the Warsaw Pact itself was in no serious sense a voluntary defensive alliance, it was the political cloak of straightforward Russian imperialism. Downsize the Red Army and Moscow would lose control of their whole defensive/colonized European fringe in very short order. To an extent, the Red Army even existed to suppress armed rebellion within the USSR itself--quite obviously in places like Lithuania, but there were anti-Stalinist uprisings scattered all through Soviet territory after WWII, and God only knows when the last of them flared up.
Khrushchev, who sincerely believed the USSR and WP in general was on the track to an economically and socially superior future, might look forward to the day in the future, some decades hence from his late 50s-early 60s standpoint, when the process of catching up and overtaking the west had gone so far that the constant rumblings of resentment against Soviet dictatorship in eastern Europe might quiet down of their own accord, and the eastern bloc nations become truly voluntarily aligned to the pact and come to see it as to their advantage. On that day, if it could ever come, he would hope the Red Army divisions might be withdrawn and disbanded at last; surely by then domestic insurrection within the USSR would be a thing of a quaint and gladly surpassed past as well. In thinking the East Germans and Poles and Hungarians and others would ever be mollified enough merely by finding themselves on the cutting edge of history, and forgive the generations of oppression and resentment (some of which to be sure, involved the desire of some Eastern Europeans to support an agenda essentially the same as Hitler's--I don't wish to over-glorify the nature of Eastern European resistance and resentment here!) Khrushchev was being way too optimistic, and as a former proconsul of Stalinist policy in Europe I suppose he was realistic enough to realize that day would be long in coming at any rate.
But aside from the inertia of an established and comfortable MIC, and the objective need of a proper military establishment to maintain a certain level of conventional proficiency, the Red Army simply had to remain massive as long as the legitimacy of Communist rule was in some doubt, which it was every moment it existed OTL.
The Red Army used a system of universal male conscription; every young man in a certain age range would be certain to be called to Red Army training and service for some years. (Other modes of service were deemed legally equivalent had at least the pretext of training up a man for wartime service--these softer modes were often the recourse of the young man from families with suitable Party connections. With these exceptions, understood as at least pretending to be an alternative mode of military service rather than any sort of exemption from it, every man born in the USSR faced the obligation to spend years in the Army). Quite obviously a big part of the expense of the Red Army was this universal service model, but consider the ideological importance of imposing sacrifice on equal terms to a Communist regime. Also of course, Soviet experience in the Great Patriotic War underscored a deep paranoia that deemed that every possible resource of defense should be developed since the enemy powers seek to overwhelm and destroy Russia completely.
Thus--even if the first generation of Soviet ICBMs, or even the second (OP's mid-60s) had been good enough to be a reliable deterrent even factoring in the possibility Western powers could decimate them and perhaps even defend against them to some extent all on their own, the Soviet regime could never seriously contemplate downsizing their military radically. They might judiciously trim it down here or there but overall the Red Army was going to be required and Soviet society was organized around it. This was not because they wished to contemplate playing pirate around the world, which was the province of Western forces, but for entirely other reasons.
And this is a large part of why and how Nikita Khrushchev was couped out (peacefully) and exiled from the Kremlin, and the Brezhnev era began.