Every major restaurant chain is eventually going to rely on electronic transactions for more and more of their business. If you talk to someone in the corporate management of one of these companies, they'll tell you that one of their primary goals is to drastically reduce the company's exposure to losses related to the handling of cash on the premises of these restaurants (incorrect change, theft, etc.).
Sickness. A complete conversion to electronic cash would definitely result in fewer sick employees. Dollar bills are NASTY, I'm sure most of us did that experiment in biology class.
No doubt that this is the goal. Hard to say if it is realistic. It never ceases to amaze me how many people don't have a bank account. They want to do business solely in cash. When necessary they pay outlandish fees for money orders and check cashing services. I don't have data but it wouldn't surprise me if this population has not become any smaller despite the commitment you describe.
I am sure a lot of this population is here illegally but by no means all of them. I've run into any number of people with no bank account who demanded to be paid in cash. Only thing they had in common was an attitude.