I always pay in cash (although I live in Canada, and not in United States as described in the article), and always prefer to be paid in cash when possible. (In some cases, the payment is shared with someone else who wishes to use a credit card for whatever reason (usually points) and I will just pay the cash to that person instead; when paying by myself, I always prefer to use cash as much as possible.)

In the example in the article: You will need to find a reverse ATM, which charges a fee, and wastes power itself (and requires the use of a card; this card may be reusable though, but if not then that is another waste), and the possible theft is not reduced (someone may steal money from the ATM) but may even be increased (someone steals it on the way, someone steals the card, someone manages to reprogram the ATM, etc) and has other problems (e.g. the ATM stops working or has no card available).

From the other comments here, it seem some places will charge more for cash and some charge less for cash.

Fortunately, from the article, it seem some states had banned cashless retail, but I don't know what is the laws in Canada relating to such a thing.