Visa and co. mostly don’t work on modern mobile phones.

Never had a problem. Not sure what that means

The networks don’t do credit, or cash back rewards, points and the like. That’s not Visa and friends. Those are offered by the banks who back the accounts. Debit cards don’t have those options and work exactly the same as far as the charge network is concerned.

The public network doesn’t have to worry about any of that. People could use it with credit, debit, or charge cards whatever they wanted.