I have no doubt that businesses will someday be cashless, I just don't know how soon it will be. It sounds eerily similar to a certain passage in Revelation:
"And he causes all, the small and the great, and the rich and the poor, and the free men and the slaves, to be given a mark on their right hand or on their forehead, and he provides that no one will be able to buy or to sell, except the one who has the mark, either the name of the beast or the number of his name. Here is wisdom. Let him who has understanding calculate the number of the beast, for the number is that of a man; and his number is six hundred and sixty-six." (Revelation 13:16-18)
Many large retailers, such as some airlines, already do not accept cash with the reported justification that "everyone" has a credit card nowadays. With further advents, such as Apple Pay, that create less of a need for carrying cash, retailers will have even further justifications for not accepting cash. Some larger retailers prefer to not accept cash to lower the chance of robbery or in-house theft.
Proponents of Apple Pay and other digital payments services argue that the future will bring us a world without a need for any cash payments at all. Sure, they say, retailers are baulking at the idea now, but give it time to mature and spread, and cashless payments will be everywhere, so much so that retailers will stop accepting cash altogether. But while I'm sure that Apple Pay will become commonplace, I seriously doubt that it will ever completely supplant payment via cold, hard cash.
People from all walks of life including politicians, the officers of companies, criminals and regular people provide demand for cash to transact business that they want to hide or keep secret. These may be innocent transactions like spending for a surprise birthday party to criminal transactions, such as dealing in drugs or bribery. People who receive money in this way want a way to spend it. Major retailers will continue to happily accept their cash in order to maximize shareholder profits.
Selling and buying of products has been possible using cashless means for quite sometime now. Despite this fact, Retailers have always had customers who kept using Cash while purchasing products and services. The advent of services like Apple Pay is no different. It should not make such a big difference that retailers will end up cashless.