I doubt GCM would be spending the money on the runway unless they had some confidence in the flight continuing - CapEx in Cayman is very much restricted right now due to UK borrowing restrictions. With the price difference between KIN and GCM, it must be working for BA or they wouldn't be able to charge such a premium?
With the new MIA automated passport machines, transiting in Miami is now very rapid for visa waiver holders however there are large numbers of Cayman Residents who don't have the right to transit via the US, and if they lost this route, would have to transit via Jamaica.
I would note though that in the current High Life magazine, GCM is marked as a seasonal destination even though current timetables continue into 2016 without a break.