Fiat money is a bubble but the probability of bursting and bubble bursting rate is very low. Money FIAT is a unit representing the economy of a country. The country's economic sectors and the type of assets it owns are guaranteed for the currency they issue. It could be called that. If the economy develops stably, the political situation is stable and they have good monetary management measures, the bubble market will not break. They may be timeless but regulated. Like some ICO projects that sell airdrops. At first the airdrop will be diluted into the market but then they will rise again.
Crypto currencies are mined or released more fragile because the individuals behind them are a group of people, a startup company. They may cancel the project or they will resell the project to another individual or company. And the FIAT money represents a nation and they seek a way for their country to exist.
Fiat money does represent a country, I think it is impossible to become a global bubble, except if the big bubble occurs only in one country, for example the economic crisis that occurred in Venezuela which resulted in their fiat currency being worthless anymore
Fiat currency reflects on what money they symbolized. It is very important for a country because economic state will see through this measures. Fiat currency bubble is more likely to not to explode or burst and can be handled and control. They are regulated properly without issues related to the management.