Yes, according to common sense and every logical analysis of human behavior, the system must eventually collapse. Here’s why it hasn’t yet ...
As long as the public believes the greenback has value, it actually does. Gold is valuable because people believe in it. At one time, spices had value as a currency.
The general public doesn’t understand what economists “understand” about why and how gold holds its value. If things got bad enough, flour would be more valuable than gold because one cannot eat gold and one can buy flour with gold only if the people who have the flour believe gold has value.
The public decides what has value and what doesn’t.
It's like a game of musical chairs. Except this time, when the music stops, everyone suddenly realizes that all the chairs have been stolen. After that...