This could work if there are reliable exchanges already available in local currency on both sides, and if both sides have bank accounts and the technical know-how to use exchanges. However, if Monero were to become a large scale method of remittance transfers, then Monero could be overvalued in exchanges in source countries and undervalued in exchanges in destination countries, especially in situations where the currencies are not freely convertible. With P2P exchanges this situation may become even more exaggerated.
Eventually HFT traders may catch on and level the market, but this would essentially mean a transfer of wealth from the masses sending remittances to a few HFT traders.
My point is, though sure it works fine in limited situations in strong economies (where there are liquid, freely exchangable fiat currencies and fair exchanges with low fees), it is a lot more complicated than it seems to use it at such a scale or in countries with underdeveloped economies.