Although ostensibly leveed against the Cuban government and Fidel Castro, the economic sanctions imposed by the United States have their greatest impact on normal Cuban citizens. Because of the sanctions (in addition to terrible domestic policies in place by the Cuban government), Cubans lack access to a host of goods and services that could dramatically improve their quality of life.
Cuba remains on good terms with rogue nations like Venezuela, Iran, and North Korea. Any profits from American trade would just end up supporting unjust policies in Cuba. The best way to put pressure on the Cubans is with sanctions. If the Cubans merely abandoned their Communist ways, America would also end the sanctions.