Dollars (and all fiat for that matter) have value because once upon a time paper money was tied to a specific weight of gold / silver stored in a bank vault. Over the past 100-ish years that link was slowly eroded until the point where there was no backing whatsoever. Inertia is the only thing keeping fiat currencies going, and it's not going to last forever now that alternatives (like cryptocurrency) exist and governments can't shut them down (like they did with the Liberty Dollar [1]).
After a couple more financial crises in the West and bank bailouts I suspect ALL governments will have limited power in this domain, people aren't going to let their savings be inflated into oblivion for the rest of eternity.
[0] https://en.wikipedia.org/wiki/Hyperinflation_in_Zimbabwe
[1] https://en.wikipedia.org/wiki/Liberty_dollar_(private_curren...