This is another reason they will be dead once these customers figure out they can do it with bitcoin faster and easier.
We're not quite there yet with seamless international transfers. I live in the UK, if somebody sends me £1,000 in BTC I need to change this into fiat money. Right now the only way I can do this is by registering on an exchange, providing all my ID + verification (sound familiar?), then listing the BTC for sale. I suspect the same is true in most countries. So Western Union still has a place until such time that BTC can be converted to and from fiat effortlessly
OR there are 1000s of retailers accepting BTC as a valid form of payment. I'm really hoping for the latter!