It makes no more sense to me than having pre-clearance at Edinburgh. How many daily flights to US can BFS sustain? If they are looking at pre-clearance it should look at LGW or possibly MAN where passenger numbers are highest. The percentage of non US passport holders at those airports is much higher than at EDI. I am excluding LHR because the logistics there would be nightmarish.
As I have said before, pre-clearance does not attract airlines as they are not greatly interested in how long it takes passengers to clear immigration.