I remember in 2013 there was a $148M bitcoin transaction. Instantaneous, 0$ in fees, no third-party involved, no currency exchanges. Granted, it was probably just moving money around the same organization's wallets, but that really opened my eyes. [1]
Someone described Bitcoin to me as the Internet of money. I'm guessing nobody at ARPA envisioned Facebook, Amazon, Netflix, or Google, but they created a platform upon which that innovation could occur. Bitcoin (or whatever) could be that platform for money.
Right now, I can see this being very useful for international remittances, like you have observed, commodity money (serving the role that gold does, as a hedge against currency devaluations, capital controls, etc), and in the informal sector esp. in the third world, where you have smartphones, but maybe not the financial institutions to bank with.
[1] https://news.ycombinator.com/item?id=6782290