With a cashless system you still have the option of paying with a credit or debit card. Most systems take some sort of wallet pay that is simple to set up on your phone.
Cash, 20 years ago, was easier to use but with advancing technology and the current infrastructure in place, cash is more difficult and provides no benefit to the consumer besides the fact that they can actually see the money they are holding. You don't get a discount because you pay in cash, besides gas stations.
Cash, from the consumer or business side, can easily be lost or misplaced. With cash a business has to safe guard bills coming in and storing bills to ready for change should the need arise. There will be daily or weekly trips to the bank to deposit cash by an employee or picked up by security guards for big box stores.
Edit: To add to this, most credit cards give you some sort of rewards, miles, cash back, etc. It is not hard to get at least 1% cash back if not more. So, for most purchases using a credit card, the net payment is less than if you were to use cash.