But you're making an assumption here that both the sender and recipient will be using fiat currency in the end, and that crypto is only being used as means to make the transfer. This is not necessarily true.
BTC is not the only cryptocurrency used there. I've sent LTC and XRP most often, but XMR lately. tx fees need not be large (also Lightning Network exists).
* Two set of fees to exchange crypto to fiat + transfer fee compared to one set of fiat currency exchange + transfer fee.