Introduction
You've asked about three different nations here, all of which have undergone extensive changes since their foundation (and one of which no longer exists at all). As such, I'll be breaking my answer down into three separate sections.
Healthcare in the USSR
Before the October Revolution, healthcare conditions in Russia were deplorable. As Reiner Dinkel said in one article on the topic:
Without doubt the Soviet Union was one of the most underdeveloped European countries at the time of the October Revolution. In terms of life-expectancy it lagged behind the other industrialized countries of Europe by a gap of about 15 years.
After the revolution, healthcare conditions began to improve rapidly. By the end of the 1960s, certain healthcare standards (such as life expectancy and mortality rates) were superior to those of more developed nations, such as the USA. Dinkel states:
One of the most striking advances of socialism has been and was generally seen to be the improvement in public health provision for the population as a whole... In 1965 life expectancy for men and women in all parts of the Soviet Union, which still included vast underdeveloped regions with unfavorable living conditions, were as high or even higher than in the United States. Such a development fits perfectly into the picture of emerging industrial development and generally improving conditions of living.
However, as time went on, health conditions began to suffer, and an apparent rise in mortality rates began in the 1970s. The reason for this is disputed, with some (such as Nick Eberstadt) arguing that it was due to a real decline in healthcare quality, and others (such as Albert Syzmanski and R.H. Dinkel) arguing that it was due to changes in statistical compilation and other external factors. In general, the healthcare system can definitely be said to have declined in quality from the 1970s onward, due to a decrease in funding and other issues.
Healthcare in Communist China
Pre-revolutionary China had absolutely appalling healthcare conditions; life expectancy was around 35 years, communicable diseases were rampant, and infant mortality rates were horrifyingly high. After the establishment of the People's Republic in 1949, conditions improved dramatically; according to a study in the Journal of Global Health:
Life expectancy soared by around 30 years, infant mortality plummeted and smallpox, sexually transmitted diseases and many other infections were either eliminated or decreased massively in incidence... By the mid-1970s, China was already undergoing the epidemiologic transition, years ahead of other nations of similar economic status.
These improvements are attributed to "population mobilization, mass campaigns and a focus on sanitation, hygiene, clean water and clean delivery," as well as "clinical care and continuing public health programs to the masses through community-funded medical schemes and the establishment of community-based health workers." This changed somewhat after the market reforms; according to the aforementioned study:
These people-focused approaches broke down with China’s market reforms from 1980. Village doctors turned to private practice as community funding ceased, and the attention paid to rural public health declined... China’s laissez-faire approach to public health placed it at great risk, as evidenced by the outbreak in 2003 of the Severe Acute Respiratory Syndrome.
While improvements have been made since then, healthcare remains excessively expensive for many people in China.
Healthcare in Cuba
Cuba's healthcare system is widely regarded as one of the nation's more impressive achievements. According to a study in the International Journal of Epidemiology:
Cuba represents an important alternative example where modest infrastructure investments combined with a well-developed public health strategy have generated health status measures comparable with those of industrialized countries... If the Cuban experience were generalized to other poor and middle-income countries human health would be transformed.
Cuban health statistics are remarkable for a nation with its level of economic development.According to a 2019 study published in the Journal of Developing Societies, some of Cuba's health indicators surpass those of developed nations, despite far lower expenditures:
While Cuba spends about one-twentieth per capita on healthcare compared to the USA... people in Cuba nevertheless enjoy longer life expectancy (79 years) than do people in the USA (78 years)... Cuba also has a superior childhood mortality rate (the number of deaths to age 5 per 1,000 live births per year) of six, compared to eight in the USA.
Most Cubans seem to approve of their healthcare system; according to an international survey in 2015, 68% of Cubans are satisfied with it. Of course, this must be taken in the context of Cuba's low rate of economic growth, which could potentially cause problems in the future. The Cuban healthcare system (impressive as it undoubtedly is) requires funding, and a higher rate of growth is likely going to be necessary in order to sustain it.
I hope this sufficiently answers your questions. Please let me know if I have missed anything, or if there are any details that require clarification.
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