Is it because of the enormity of the tragedy playing out in the western part of the island of Hispaniola that the pronunciations being used by the BBC have been standardised so quickly? Has the management sent down an edict that the established anglicisations be used for both the name of the state and that of its capital, so that no time need be wasted arguing with viewers and listeners, or internally, about the rights and wrongs of alternatives?
I’ve heard virtually no renditions of Haiti as /ˈɑːiːtiː/, but only /ˈheɪti/. As for the capital, very rarely has anyone uttered an attempt in my hearing at the word Prince with a French pronunciation. The usual ‘error’ is to call the capital /ˈpɔːt əʊ ˈprãs/, in the mistaken belief that this is the French pronunciation, but in French there is no liaison of the /t/, so the usual French pronunciation is /ˈpɔːr əʊ ˈprãs/ /ˈpɔːr o ˈpr̃ɛs/. (I’m sorry I’m using [ã], but placing a tilde above [æ] or [ɛ] is too much effort). /ˈpɔːt əʊ ˈprɪns/ has a long pedigree in English, and there is no need to replace it at this juncture.