That's correct. However, as Block is already demonstrating with Square/Cashapp, bitcoin payment rails doesn't have to mean that payers and payees necessarily have to ever even know that their fiat payments were transmitted as Bitcoin.
What I'm asking for is that the payment rails be via decentralized, permissionless, more cost-efficient Bitcoin - with voluntary usage of services that offer bridges from/to fiat (e.g. cashapp, square, etc) for those who just don't want to hold bitcoin due to volatility (or any other reason), rather than reinfocing the backwards status quo of the other way around.
PS. I do think bitcoin volatility will continue to drop, but I personally don't believe it will ever be as stable as the U.S. dollar is now, for example... After all, it's way easier for a centralized authority to manage a slow leak of value in the dollar than it ever will be for a free market to stabilize the exchange rate of Bitcoin.