It's already happening in some countries that are in economic turmoil, such a Venezuela, where their own fiat currencies have become practically worthless;
people there are turning to Bitcoin just to survive and buy food. And, if you look at what's happing economically around the world -- Brazil, Zimbabwe, Greece, to name but a few -- many countries are already heading for the same fate. When you consider that the global economy is a complex balance of individual economies, like a delicately balanced stack of playing cards, it doesn't take much to upset the balance and bring the global economy crashing down, bringing those at the top with it.
Studying cryptocurrencies makes you think really hard about what money is. We take money for granted but it's not until you start to wonder where the value is in cryptocurrencies that you start to question where the value in fiat currency is. You begin to realise that the world's economy is backed by nothing but governmental promises. It's a fragile mess, an enormous Ponzi scheme even, of money printed at will, creating ever increasing inflation (aka devaluation of your wealth). It's entirely unsustainable and, without wishing to sound like some 'end of the world is nigh' nut-job, I believe what we're witnessing is the beginning of a global economic collapse .... or at least a collapse of the 'present system'. As more people rush to move their wealth into cryptocurrencies, it's likely to accelerate that collapse very quickly, meaning it may be coming far sooner than any of us think it is.
The attempt by banks and governments to make their own cryptocurrencies is interesting. It demonstrates defeat ("if you can't beat them, join them"). The blockchain itself is nothing special; it's just a type of database or ledger. The banks already have those, and they already have digital money. What makes cryptocurrencies like Bitcoin special is their decentralised nature, the fact they're inherently secure (no single point of attack) and that nobody can control them or manipulate them. To create a centrally-held, government/bank-controlled cryptocurrency is to completely miss the point.
And here's where it gets really interesting: If all the wealth in the world eventually moves onto distributed, decentralised blockchains, away from governmental control and manipulation, not only do banks become obsolete, but so does government. If we separate money and state, the state loses its power. No longer can a few individuals decide how much of your money should be spent on war, healthcare, policing, etc, etc. Personally, as a proponent of technology, I like the challenges that presents and I look forward to a world where consensus rules through software and technology.