Is there any widely accepted downsides for Cuban system? The Cuban political, social and economic systems under communism are known for having a good medical system and high quality medical workers. Cuba also has a good educational system. The country also provides most public services (as is typical in communist or formerly communist countries).

Some fragilities of the Cuban system include patients leaving the country to obtain medical care to obtain higher-paying employment opportunities and other life conditions.

Notwithstanding, are there any disadvantages of the Cuban economic and social system that are largely accepted by:


University literature
Actual speeches of the Cuban government
Cuba-based media
Media interested in Cuba but based in foreign countries


Those downsides could be of any form, like poverty, corruption, bad quality or quantity in first-need objects....

EDIT:
To narrow down the question and make it more specific:


Is Cuban economy mainly based on what government provides, or have Cubans enough purchase power to buy "what they want"?
Did company-based economy develop? Like if I want to create a company for a specific application, it is feasible?
Is food available for middle Cuban classes at correct prices?
Are importations possible or too expensive ? If not, why are they expensive: transportation costs, government taxes?
The Cuban system is widely criticized. Particularly by people who experienced it.

(Aside: In fact, this is consistent with the general trend that people who have actually lived under Communist, Socialist and Marxist systems tend to condemn those systems. And the only people who tend to praise such systems are people who never lived under those systems yet favor imposing those systems on others against their will.)


roughly 1 in 10 of all Cubans choose to live in the U.S. (despite the extreme hardship of making that migration)
roughly only 1 in 100,000 Americans choose to live in Cuba (despite the relative ease of making that migration and many of whom are FBI fugitives, avowed Communists and members of other radical leftist organizations)


Notwithstanding the above observations and statistics, let's study two of the question's premises.


  Cuban medical system is as far as I know well known for the quality of its formation and the medical workers and doctors it gave. Cuba has also a good educationnal system.


While it is true that the medical system has been praised. Many criticize the praise as being inaccurate. For example, this research paper from the University of Miami in 2007 cites:


  My own research, however, suggests that the unequivocally positive descriptions of the Cuban health care system in the social science literature are somewhat misleading. In the late 1990s, I conducted over nine months of qualitative ethnographic and archival research in Cuba. During that time I shadowed physicians in family health clinics, conducted formal and informal interviews with a number of health professionals, lived in local communities, and sought to participate in everyday life as much as possible. Throughout the course of this research, I found a number of discrepancies between the way the Cuban health care system has been described in the scholarly literature, and the way it appears to be described and experienced by Cubans themselves. [emphasis mine]


Further, the author writes:


  After just a few months of research, however, it became increasingly obvious that many Cubans did not appear to have a very positive view of the health care system themselves. A number of people complained to me informally that their doctors were unhelpful, that the best clinics and hospitals only served political elites and that scarce medical supplies were often stolen from hospitals and sold on the black market. Further criticisms were leveled at the politicization of medical care, the unreliability of health data and the overall atmosphere of secrecy surrounding the prevalence of certain infectious diseases such as HIV and tuberculosis.


We know that Socialist, Communist and Marxist regimes are not transparent with their information. So many consider the official reports of the quality of Cuba's health care system to be unreliable at best.

Perhaps the most objective indictment of the Cuban system, however, is to look at migration patterns into and out of the country.

In 2017, the Migration Policy Institute reported findings that: 


  Cubans have been among the top ten immigrant populations in the United States since 1970, and in 2016 were the seventh largest group. Nearly 1.3 million Cubans lived in the United States in 2016,


Further, they report:


  Compared to the overall foreign- and U.S.-born populations, Cubans were less likely to be proficient in English, had lower educational attainment, and earned lower household incomes.


Researching migration patterns in the opposite direction: from the U.S. to Cuba, I found this Wikipedia article which estimates there were nearly 2,000 to 3,000 Americans living in Cuba in 1998. And that many of them were FBI fugitives, avowed Communists and members of other radical leftist organizations.

The fact that roughly 1 in 10 of all Cubans choose to live in the U.S. (despite the extreme hardship of making that migration) and roughly only 1 in 100,000 Americans choose to live in Cuba (despite the relative ease of making that migration) is a very objective and quantitative indictment against the Cuban system in addition to the more qualitative indictments provided from the above sources.