For me, i do not think bitcoin can replace fiat totally, because when their are larger transactions to be processed, it takes hours or even a day, except you have to pay Higher fees to process your transaction.
Fiat has been here for a long time, and will be around for a while until it is completely replaced by digital currencies. The question is only how many years or decades will it take to completely disappear from use.
The big transactions you mention are not a problem for crypto, you can send $1 dollar or $1 million in BTC, and it just depends on the fees when the transaction will be confirmed. Only thing that we need to pay attention is size of transaction (number of inputs/outputs), and to use SegWit if we want to save on fees. If your transaction is had 1 input/2 outputs (standard transaction), you will pay same fee regardless of the amount you send.
On October 16, a Bitcoin user moved 29,999 BTC worth $194 million with a $0.1 fee, a transaction which with banks would cost tens of thousands of dollars. An often pushed narrative against cryptocurrencies like Bitcoin and Ethereum is that it is expensive to clear
As you can see from the example above, transactions in crypto can be very cheap, but you need to consider all the key factors when doing payment with crypto. If you need instant transaction, check current fees and apply them - if you can wait, just go with lower fees.
I use Bitcoin as currency, but also as store of value, one does not exclude the other, and this is one of the great advantages of Bitcoin.