We dont need actual fiat currency eur/usd...we should be start using stablecoins like fiat currency.
Fiat is backed by the government of the country that is issuing it, but you want it to become things of the past when the government are piloting and creating CBDCs which are also fiat. It is easy for me to convert bitcoin to fiat whenever I am in need of money, which I think is all I need.
I understand you very well though, you want cross border transactions to be easily accessible and cheap, which can be a means fiat pegged decentralized currencies can help, but not only fiat pegged coins that can help, also unstable cryptocurrencies like bitcoin is good for such purpose as well.
But it the card needed? No. I have easily make payment on sites (be it local or foreign) that are accepting cryptocurrencies easily using a very cheap amount of fee. But what I still find difficult is that some sites still do not accept cryptocurrencies as a means of payment.