I think the complete opposite would happen if Bitcoin replaced fiat which won't happen anyways as already noted above. Because when fiat is replaced by digital money the physical money would become obsolete and thus worthless. Their value from a collector's point of view will plummet because there would be no interest in keeping such outdated artifacts any more.
banknotes and legal tender coins (nickels dimes, cents, 20p pieces and pennies) will be useless..
but asset collectables (1ounce gold coins) will have a place.
it wont be a big place. but will see growth of utility. just like bitcoin.
not due to bitcoin being a one world currency. but because fiat becomes hyper inflated and people are peed off with having to work an hours labour and have their wife stood at a grocery aisle to spend it before the hyper inflated fiat the guy worked an hour to earn is not worth a loaf a bread.
people will still be in the majority forced to work for fiat due to legal tender laws of tax/minimum wage etc. but they will convert it to more stable currency for long term handling.
again not everyone will do it. and bitcoin/gold wont replace fiat. but it will become a open choice to swap into