There’s nothing that makes it inherently impossible to put bills this way in cash, though.
For example, in Japan, you can pay bills by taking them to the local konbini - which is probably no more than a couple minutes walk away - then handing them the bills. They scan barcodes, take your cash, stamp the bills, give you your change. Done. No need for ID or a bank account.
The reason that people can’t easily pay bills in cash in the US is not because it can’t be done.
For example, in Japan, you can pay bills by taking them to the local konbini - which is probably no more than a couple minutes walk away - then handing them the bills. They scan barcodes, take your cash, stamp the bills, give you your change. Done. No need for ID or a bank account.
The reason that people can’t easily pay bills in cash in the US is not because it can’t be done.