As far as I can tell, there's no reason to believe fiat currencies/economies are headed for any kind of collapse.
Sure there is: the simple mathematical fact that an ever-increasing expansion of debt (which the current system is based on) is unsustainable.
Debt is just a number, a value stored in a computer database. A number can get as big as you want it to get. If you were talking about exponential growth in the use of resources or energy, etc, I'd agree, that's mathematically not possible to sustain forever. But if we're just talking about currency/debt, the numbers can just as easily be quadrillions as billions, can just as easily be 10^100000 instead of quadrillions, and society will look no different.