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.