For me, if ever BITCOIN will surpass the value of fiat money. Fiat will still stay and Bitcoin too. Some may not be comfortable using Bitcoin for their daily lives or in some cases payments. Some people may only buy or use Bitcoin as their investment, a store of value.
As I saw on some country with their fiat become useless with the hyperinflation just like Venezuela, their fiat becomes useless but I believe that they will recover, some people there already using Bitcoin but some don't want it or they don't have any idea what Bitcoin is.