by 2022? in 6 years? Hardly so...
by 2030 - yes, very likelly.
by 2050 - VERY sure. Not even small doubt. FIAT will be found only in the history books by 2050
Even in 2050, bitcoin cant replace fiat. Bitcoin is a global cryptocurrency and cryptocurrency cant just replace fiat currency.
Each country has its different fiat currencies. Its necessary for the economy of the world. In 2050, perhaps paper money can replace digital money like paypal, pm, etc but it will be according to each nation. Whole globe cant have one single global currency.
And even if we do have one single global currency, it will just cause chaos to people. Those that have the most bitcoins will have the most power. The country that holds the most bitcoins will surely become the most powerful country. Money controls things so the government wants to have control of money. With bitcoin, they can't do their magic of nonstop printing it. They wouldn't be able to manipulate the people, they wouldn't even be able to collect tax from people.
If you guys have watched the famous TV series called Mr Robot, you will see that even in a fictional world, the government hates bitcoin because they have zero control over it. In the tv series, they also have a cryptocurrency but not a global one.