but nobody can exclude Fiat currency because it exists within the market
Crypto also exists within the market, if I am understanding your statement correctly. It is just that crypto has a cult followership and not a bigger market share than fiat.
you're right that crypto was already fiat
That is a wrong usage of words. Fiat is used to denote the currencies that these world countries have been using as mostly paper bills and includes the digital payments too that are in those currencies. Bitcoin came in 2009 and then it was an alternative method of transaction.
and employed by people Fiat lost its place after the crypto arrives but now many are fiat currencies.
Wrong statement. Fiat never lost its place but lost a very small part of its market that was taken by crypto. But that small part is almost negligible as per statistics.
That's why we both need work If crypto may be a fiat currency then we'll be privately owned in two ways.
A decentralized currency cannot be privately owned but a centralized currency is controlled by certain institution(s). That is why the community likes to go for the decentralized coins like BTC over the centralized ones like Ripple.