I don’t think the visa is as much of an issue as is having to clear customs/immigration in Miami. Many Caribbean based travelers have US multi year, multiple use visas anyway as they also travel to the US itself. Even people who don’t travel to the US frequently tend to keep it up to date just in case. The biggest headache has always been the reconnection through Miami but with the updated kiosks even that has been improved somewhat. I agree with you though that people who don’t already have visas are highly unlikely to get one just to make those trips. However for those going Eastern Caribbean to Western Caribbean and vice versa, I’m not sure the subset of people without US visas is that high.
I am not sure that one can say that Jca E/C bound passengers are mainly the upper middle class types (business people or gov't officials) with multi entry visas. Given the difficulties that many J'cans have in their travels to the E/C this is a more diverse traveler than maybe it was 30 years ago. Jamaican populations do now exist in many of these islands, triggering levels of VFR travel. Shanique Myrie might be more of a norm than one would think.
Using the kiosks doesnt automatically mean that one doesnt have to join the line. Then especially in the summer many of the northbound AA flights are late, meaning that a 2 hour gap, which should be enough, suddenly becomes a race. Of course the infamous "waiting for an open gate". Aside from those who want to build their AA FF miles I just dont see how it is easier to fly KIN POS via MIA. Its approx. the same fare and 3 hours more (if all goes well).
For people traveling to MBJ, GCM and NAS I can see the advantage. For POS bound out of NAS its pre clearance so the hordes at MIA (CBP and TSA) you dont have to deal with. Even though BWs one stop is still more convenient, though more expensive. NAS to BGI will be easier on AA for those with multi entry visas.