You missed the entire point of Bitcoin - allowing individuals to transact securely across distances without the need for a third party. The blockchain (the entire network) secures the transactions.
I hope we eventually have a blockchain that could serve both purposes.
There are specific instances where people do not have remittance services available to them -- getting money across some borders, completing illegal transactions, etc. For BTC to be a mainstream money transfer method, however, it will need to be obviously better than just doing it the old way -- paying a 3rd party to clear the transaction.
It's an elegant technological breakthrough in search of a killer app, I think, and that killer app can't just be illegal or extralegal transactions. If that's all it ends up being, governments are going to crack down even more than they already have.
It's not a technology problem. Transfers could be instantaneous and nearly free without a blockchain. The reason they are not is because of several reasons. Fraud prevention is one. Another is that the cash being held during the transfer is used for investments.
Bitcoin makes this faster because there is no middle man or regulations slowing it down, not for technical reasons.