GA pilot reported on final approach to a non towered airport; they had a NMAC with a light aircraft approaching from a base leg.

Narrative

On final approach to the ZZZ airport I had a close encounter with a small taildragger resembling a Piper Cub. I was approaching the airport from the north and entered a long final. Traffic calls were made at 12nm; 8nm; and 4nm from the airport. An aircraft to the south responded so I know that my radio was functional. On approximately a 1 mile final I looked to my left and saw a yellow aircraft completing a turn to left base. Fortunately due to the difference in our speeds I was past him before we collided. After landing I mentioned the aircraft to the FBO personnel and was informed that the gentleman flying the yellow aircraft was an experienced pilot but did not fly with a radio in his aircraft.It is beyond me how the FAA can continue to allow pilots to operate in US airspace without a radio of some type. I have flown numerous aircraft without electrical systems but I always have a handheld radio connected to a headset. The FAA MUST do something to correct this issue. Numerous times in my career this has occurred. Any pilot that can afford an aircraft of any type can easily afford a $200 handheld radio and a headset. Please don't just dismiss this plea. This is one of the easiest issues to fix for very little cost to the pilot. Don't allow this stupidity to continue.