Source: Library of Congress LC-D4-16345.
By the late 19th and early 20th centuries, cold chains began to be set. The banana trade was an important driver of this transformation since it represented a perishable good that could be produced in large quantities and thus required mass conveyances. As long as the cargo could arrive in good condition to consumption markets, buyers could readily be found. Thus, the banana trade was dominantly constrained by distribution more than by supply or demand.
By the late 19th century, the mass consumption of bananas in the United States became a reality with the setting of supply chains, including production (plantations in Latin America) and distribution facilities. The United Fruit Company (which later became Chiquita) and Standard Fruit and Steamship Company (which later became Dole) were the first major actors involved.
In the above photo, unripe banana bunches are being manually unloaded from a ship at the port of New Orleans, where Dole was based. A refrigerated rail car (using ice as a coolant) is waiting to be loaded and bring bananas to inland consumption markets (up to Chicago). This was a labor-intensive process prone to spoilage.