Are you sure it was "capitalism" that led to the "collapse of trust"? Did Soviet citizens trust the local healthcare system when the quality of care you received depended on your party rank?
From a Wikipedia article on the Soviet healthcare system[1]
"Many medical treatments and diagnoses were unsophisticated and substandard (with doctors often making diagnoses by interviewing patients without conducting any medical tests), the standard of care provided by healthcare providers was poor, and there was a high risk of infection from surgery. The Soviet healthcare system was plagued by shortages of medical equipment, drugs, and diagnostic chemicals, and lacked many medications and medical technologies available in the Western world. Its facilities had low technical standards, and medical personnel underwent mediocre training. Soviet hospitals also offered poor hotel amenities such as food and linen. Special hospitals and clinics existed for the nomenklatura which offered a higher standard of care, but one still often below Western standards"
I think the problem more generally is that of adverse incentives, whether in "capitalist" or "socialist" systems. I worked in the UK National Health Service which is "free at the point of use" which often results in rationing via waiting list. In my experience, many patients believe that their GP is inappropriately limiting their treatment to save money, particularly with respect to limiting testing, which is unsurprising because "gatekeeping" is often an explicit responsibility for general practitioners in the NHS [2][3]
Everything you're saying about the Soviet health system is true of capitalism's health system now. The difference is that, in the US, we go into debt for our mediocre care.
The main reason for the discrepancy in care quality during the midcentury is... drumroll please... that the Soviet Union was poor, due to initial conditions. It encompassed countries that had long been impoverished. The US had a middle class to build on; the USSR did not. It built a middle class where none had ever existed. Not to mention, the US was in the historically rare situation of winning a war (since, in economic and humanitarian terms, wars are negative-sum and most often only have losers). The USSR, on the other hand, consisted of nations that had taken a beating in World War II.
If you compare Kyrgyzstan to Alabama, the Soviet Union looks bad, but that's not really a fair comparison. Capitalism, as a sea empire, could dominate people from afar and keep them in nominally separate nations while exacting tribute; the Soviet system, as a land empire, could not. It had to integrate them. That's a harder problem. If you make a fairer comparison--say, if you compare Kyrgyzstan to Honduras or Haiti, the picture lines up a lot better. I imagine the quality of healthcare in the poorest countries under capitalism's thumb is even worse than it was in the poorest SSRs as of 1989.
This isn't to say the USSR was great. It was an authoritarian regime, and it launched some really ugly wars (such as the one in Afghanistan). It remained poor (relative to the West) throughout its lifespan because, ultimately, there is no magical economic system that guarantees 12% annual GDP growth--doesn't exist, never has. Socialism solves one set of problems--and a big set of very ugly problems--that capitalism lets fester, but does it automatically bring about utopia? No, not even close. On the other hand, socialism iterates toward a better standard of living for the common people; capitalism, unless heavily checked (as it was in the Cold War) iterates toward a worsening standard of living. So, on that dimension alone, capitalism loses. Everything said above about shortages and nosocomial infections and substandard care applies to capitalism's medical system today.
From a Wikipedia article on the Soviet healthcare system[1]
"Many medical treatments and diagnoses were unsophisticated and substandard (with doctors often making diagnoses by interviewing patients without conducting any medical tests), the standard of care provided by healthcare providers was poor, and there was a high risk of infection from surgery. The Soviet healthcare system was plagued by shortages of medical equipment, drugs, and diagnostic chemicals, and lacked many medications and medical technologies available in the Western world. Its facilities had low technical standards, and medical personnel underwent mediocre training. Soviet hospitals also offered poor hotel amenities such as food and linen. Special hospitals and clinics existed for the nomenklatura which offered a higher standard of care, but one still often below Western standards"
I think the problem more generally is that of adverse incentives, whether in "capitalist" or "socialist" systems. I worked in the UK National Health Service which is "free at the point of use" which often results in rationing via waiting list. In my experience, many patients believe that their GP is inappropriately limiting their treatment to save money, particularly with respect to limiting testing, which is unsurprising because "gatekeeping" is often an explicit responsibility for general practitioners in the NHS [2][3]
[1] https://en.m.wikipedia.org/wiki/Healthcare_in_Russia#Early_S...
[2] https://www.theguardian.com/society/2001/sep/15/NHS
[3] https://bjgp.org/content/69/681/e224