There are transit systems that literally do not accept cash. The light rail trains, trolleys, and to some extent BRT all come to mind in Seattle.
And you can totally pay cash on the RapidRide buses, you just have to board via the front door of the bus. (If you pay with an ORCA card you can board via the back door if you want to, but if you're paying cash you have to board normally).
For BRT, you can pay cash at the time of boarding.