Kosygin becoming the most powerful member of the politburo almost certainly is a major boost to the Soviet Union. Probably it saves the Soviet Union - but not necessarily. The Communist party is a load-supporting element of the whole structure and if a leader like Gorbachev comes to power and undermines the party, some sort of collapse is inevitable even if the economy is stronger.
Kosygin has several advantages over any other possible candidate: as leader, the Soviets can resist going into Afghanistan, spending on farming will not skyrocket (Kosygin was firmly on the side of the cities and wanted to focus most investment on urban areas and industry which would have been far more useful at that point in Soviet development), Kosygin was also a man with actual managerial experience - which was rare in the upper echelons of the Party.
Kosygin being powerful might also abort the rise to power of Suslov's creatures - Andropov and Gorbachev (yes, Gorbachev was the protege of archpriest of Communism and leader of the hardliners - there's a reason why his ascent to power scared most Kremlin-watchers in the US so much). This would have unpredictable effects - OTL the Party was dominated by Brezhnevites (easygoing, moderate and corrupt pragmatists) and the "Stalinists" (who were not actually very Stalinist and tended to have a wide range of views, mostly united by not being as easygoing as the Brezhnevites - no surprise that members of this group tended to advocate reform in the areas they delt with - also no surprise that they opposed reforms of the sort that Kosygin advocated, that weakened centralization).
As prior posters have pointed out, however, getting Kosygin into power is extremely difficult, since the man also had a number of disadvantages. For one, his idea of reforms appealled to no significant political group in the Party. For another, Kosygin doesn't seem to have had that much personal ambition. For another, he had actual managerial experience - this was rare in the Party and hence was a reason for more normal Bolsheviks to hold him in some contempt. Kosygin also seems to have lacked the same political skill that Brezhnev had.
I think the best chance to get Kosygin's ideas to win is to have Brezhnev continue to be a firm ally. The second most likely way for his ideas to win is for a Kosygin-Podgorny alliance to either oust or achieve favorable power-sharing with Brezhnev.
But if the Soviet Union does conduct Deng-style reforms in the early 1980s, then it would be powerhouse, Russia today IOTL still has a much higher GDP and income per capita compared to China. And it has massive resources and technical expertise.
Kosygin's ideas on how to reform things was very different from Deng's ideas (no surprise, since the USSR had very different problems to those faced by China).
Unfortunately, while the Soviets did have massive resources, most of them are positioned in very inconvenient locations. A major driver of the economic malaise the Soviets suffered from was the need to spend massive amounts of resources building the infrastructure to access Siberian resource deposites even as the resources in the European USSR were depleted.
The Soviet Union was suffering from an energy crisis.
No doubt that Kosygin's ideas could have really improved things though.
Kosygin, though, was no Deng. I read up a little on his reforms, and they were closer to Titoism than modern China's so-called socialism. Its much better than the Brezhnev attitude, but its no surefire fix for the USSR's economic stagnation.
It is useful to note that the Soviets, even in their "stagnation", were showing levels of economic dynamism we would kill for today. Their stagnation was a
relative stagnation (mostly in comparison the the USA at that point). As such, a USSR that crawled along at the
real growth rate they'd achieved in the late 70s up until the present would look like it was doing pretty well.
On the other hand, higher birthrates in Central Asia are going to be problem no matter what, if nationalism or Islamism gains a foothold in these areas, game over, hence the necessity of totalitarian controls. Turkic and Iranian peoples were projected in 1985 to outnumber Russians by 2000. I want to emphasis on how this probably the most serious challenge in keeping the USSR together
The growing Central Asian population would certainly have posed problems - but not, I think, problems with nationalism or Islamism. The main threat is from Russian fears about being swamped by the "other" (and Russian racism then making the Central Asian peoples feel like they can't make it in the USSR).
1) Khrushchev's coup was led by Stalinists - Suslov, Brezhnev, Podgorny, Shelest. The likelihood of this crew enacting Kosygin's reforms is rather unlikely. The whole clock pendulum idea.
Calling any of these guys "Stalinist" is problematic. Suslov probably qualifies for the label best, but even he seems to have had no interest continuing or re-implamenting the purges or personality cult that were so central to Stalinism. Brezhnev I've seen described with any number of political labels, from liberal to moderate to hardliner - I think the best description of him is actually "easygoing". Podgorny I have seen lionized as a liberal (to me Podgorny seems to have been very interested in his own power and willing to do whatever it took to increase it in a given situation). Shelest is mostly remembered today for his encouragement (however cautious) of Ukrainian culture (not something Stalin was famous for at all).
And calling Krushchev a "liberal" is just as problematic, given how illiberal (nay, Stalinist) he was in some ways.
Really, I think any of the factions Kremlin watchers and historians have tried to apply to Soviet politics seem to mislead more than they inform.
3) The discovery of energy reserves in Western Siberia probably killed them. Google "resource curse" or "Dutch Disease". Once they discovered oil and nat gas, it was too easy to allocate scare resources toward energy reserves, particularly during the 70s, rather than enact needed reforms. This happens everywhere - Mexico, Venezuela, Iran just to name a few.
The exact economic mechanisms were different to "Dutch disease", but it is true that the USSR probably over-invested in oil and gas in the 70s leading to a very similar sort of malaise.
4) I can't recall the source but I read where Kosygin never wanted the top spot. Didn't want the power and the risk that came with it.
I am also not remembering sources, but this matches my memory.
5) Military spending would need to be curtailed early on. It sucked up far too many resources from the economy. It's hard to see this happening, particularly after the Sino-Soviet split.
Less military spending would have helped a little, but military spending was not actually the problem it has been reported to be, Gorbachev in particular seems to have inflated the military spending problem in order to achieve political goals and to cover other economic failures of the regime.
Both Allen and Hanson show quite convincingly that military spending was not a statistically significant drag to the Soviet economy and Hanson has shown that the regime was in fact able to reduce military spending if required, even when the Cold War was at its hottest.
6) Too many bright minds were either eliminated or permanently scarred by Stalin's purges. Bold initiative was too scarce or affected incompetently.
Not only this, but then WW2 also slaughtered capable Soviet citizens in vast numbers. There is no doubt that the double whammy left the Soviets without enough flexible minds to deal with the challenges they faced anywhere near as well as they could have.
Even in the capitalist economies of Europe, full economic recovery from WW2 did not happen until the
1980s. And except for Germany, none of the capitalist economies had suffered anywhere near the casualty rates as the Eastern Europeans had (including the USSR). And in the German case, the massive losses were balanced somewhat by the influx of German-speaking refugees from across Eastern Europe.
fasquardon