What does Florida have against Cuba? I sure there's some who would like to visit. And other would have family they could visit. Also Florida would be a popular destination for Cuban tourist if they can afford it.
When Castro overthrew the unpopular and corrupt regime, a lot of Cubans who were better off under it and faced bad things fled to the US. Anyone who just didn't like Castro fled to the US if they could. It created a pretty passionate group of Cuban exiles here, who when they weren't working for dirty CIA operations and Bay of Pigs invasions and a Watergate burglary team, pretty loudly said they did not want any policies friendly to Castro.
But I do suspect that nowadays, things may have changed on those politics some.