What if somebody started handing out coupons for Bitcoins. It's just a piece of paper, with security measures and all, saying "If you give this back to me, I will give you 0.001 Bitcoin". If that catches on, we'd effectively have a normal currency, backed by something no government can just print arbitrarily. That's just like any currency back when we had the gold standard, when money was literally just a voucher for gold.
Now, that does present a tremendous difference to today's economic system, where currencies aren't backed by anything other than governments, which have the sole power to print them, and each currency is also indirectly backed by its economy: if it's doing well, more people will want to have that country's currency. If for some reason the dollar was worth 1000€ tomorrow, then all American investors would buy Euros to invest in things with in Europe, which would greatly increase the value of Euros again and soon the Euro is worth as much as it "truly" is. If your economy has a weak economy that leads to less demand for your currency, meaning because of its low price more people will buy your currency and then invest in your country with that currency. In a way this dampens the effect a weak economy has on outside investments, it creates a more level playing field between countries on the international market, through a natural balancing force
If tomorrow the entire world started using only Bitcoin or gold (Bitcoin is really just a fancy digital version of that), then we wouldn't have that natural balancing force. Everyone having the same currency leads to poor economies doing poorer, if you don't believe me look at what the Euro has done to Greece, Spain and Portugal, their GDPs are dropping rapidly for years. But under that common currency, rich countries will do even better than before, because they can then export to those other countries more cheaply than they would with seperate currencies, while they're importing less from there, meaing poorer countries will get an increasing trade deficit, making them poorer and poorer, with no bootstraps to pull themselves up from.