Cash was the gold that you used to be able to redeem said liabilities for. These days, you can simply transfer the bank's liability to you to someone else, as a way to offset your own liability.
Just because the bank has no intention of ever paying cash at this point ever since Nixon left behind specie payments doesn't change the fact that these notes are still issued as liabilities.
And when I say issued by the central bank, I do mean only the paper bills that are issued. Most money that exists in bank accounts is issued by the various commercial banks that operate within the banking system (when they issue you a loan, they don't go out and find other money; they simply credit your account with the amount of the loan, and that money was simply loaned into existence as a liability of that bank).
There is intrinsically no difference between deciding gold is the scarce thing that we all accept as money, or some specific hard to duplicate paper money. They both serve th same purpose.
Whether bitcoin is used for direct payments or payment channel settlements is irrelevant. What is important is self-custody. Cash works and has the properties it does because it is a (mostly) fungible bearer bond. Bitcoin is also a (mostly) fungible bearer bond regardless of whether you transact on chain or through lightning.