Who said it didn't?

The fact that the Caribbean was colonized at all was entirely the result of maritime transportation, though the ship size and level of maritime technology wasn't on par with other Old World maritime cultures (including China).

For a long time it was thought that Arawak speaking peoples island hopped from roughly the region around modern day Venezuela, along the Lesser Antilles, finally ending up in the Greater Antilles last. However, more recent research suggests that these peoples (often known as the Taino) appear to have gone straight to the Greater Antilles, either skipping or at least not making permanent settlements in the Lesser Antilles. This is due to the fact that we don't really have much evidence for their presence in the Lesser Antilles, but have tons of evidence for their presence in the Greater Antilles. Though to be fair, it may just be that we haven't come across their settlements in the Lesser Antilles. If they did go straight to the Greater Antilles, this meant traversing the Caribbean South-North. As Fernand Braudel points out in The Mediterranean and the Mediterranean World in the Age of Phillip II (concerning the 16th century), even most Mediterranean maritime cultures rarely traversed the open sea, instead preferring to hug the coasts for the most part. Most maritime trade was coastal, which helps explain the power, wealth, and influence of coastal cities and the city states or feudal lords who ruled them.

There appears to have been trade with Meso America, as weapons particular to Meso America have been found in Taino settlements in the Greater Antilles but the workshops and tools which produced these stone weapons are nowhere to be found in the Caribbean.

There also seem to have been settlements in the Turks Islands to the North of Cuba and East of Florida. The settlements there don't appear to have been permanent, instead focusing on local resources used for dyes which, once collected, were transported elsewhere.

In both cases, this means trade and demand for products. It definitely looks like there was trade with both the mainland to the West (modern Mexico and the Central American Republics) and to the South (modern day Colombia and Venezuela). In addition, the Guanahatabey people of Western Cuba appear to have been originally from Florida while the trade in precious ceremonial resources in the Turks Islands suggests that trade networks went that far as well.

There were also political systems with varying degrees of stratification. Hispaniola (modern day Haiti and Dominican Republic) seems to have had a fair number of chiefs who in turn gave tribute to other chiefs. Wars were organized at times as well, often using canoes to transport raiding parties.

Without getting too much into the controversy of the Carib peoples of the Lesser Antilles, they are also alleged to have used massive canoes filled with dozens of people in raids.

Part of the problem is that these were societies which had not yet adopted writing systems and many of the people who would have known about these trade networks and maritime conflicts. Because we have almost no written records and the few that we do have are often very influenced by the prejudices, language barriers, and political intentions of their authors, our understanding of the pre-Columbian Caribbean is profoundly warped and fragmented.

As archeological research continues, in spite of the lack of funding, hopefully we'll find out more and have more of these theories confirmed.

If you're interested in reading the classic text on this, you can read Irving Rouse's The Tainos: Rise and Decline of the People Who Greeted Columbus, written in the early 1990s. This is unfortunately almost 30 years out of date and the scholarship questions a lot of his ideas. For a more recent take, I strongly recommend William F. Keegan and Corinne L. Hofman's The Caribbean before Columbus as well as Keegan's Taíno Indian Myth and Practice: The Arrival of the Stranger King which dives really deep into the topic of the Taino in particular.

Hope it helps.

Edit: Also, a while back we did a great podcast episode with Dr. Antonio Curet of the Museum of the American Indian in DC. You can listen to it here, though admittedly we don't get too much into maritime tech as I recall.

Followup question: how much do we actually know about pre-columbian Caribbean civilization? My understanding is that disease initially wrecked populations and then the moment europeans started settling, disease came in for the final kill. Weren't islands like Haiti entirely devoid of natives only a few decades in?