I suppose by the early 1960s radio demand would have weakened and the fixed AC powered product would either be a novelty item or a bedside alarm appliance.

The first example I have is a 5-transistor GE brand using actual GE transistors: It has a miniature tuning gang [TRW brand] connected with a dial cord arrangement. It also has a complex AC clock/alarm mechanism. It might just be about GE's last hurrah at domestic manufacturing! Its transistor power is from a small transformer, half wave rectifier to single-ended O/P transistor with heatsink.

The GE Transistor Manual of 1964 gives examples of AC radio designs and on page 282 has this to say:
"The most economical design, the Four Transistor Line Set...Incorporation of a Class A output stage with its constant current drain permits the use of a simple half wave rectifier and dropping resistance. The resistance may consist of a light bulb, a high resistance line cord, or an actual resistor. Even with an inefficient power supply of this nature, power consumption of the transistor set is only one third that of a tube set. Sensitivity, selectivity and audio output of the transistor receiver are all equal or superior to an equivalent 5 tube AC-DC radio."

The second example is about as cheap as an AC radio could be made: Made in Taiwan for next to nothing, it only has 4 transistors and a mere single screw for the back cover! Power is simply derived from the AC line with a single .01μF 1.4kv ceramic capacitor and two resistors (470 & 3.9k) + a single diode. The capacitive reactance [xC] at AC frequency comprising part of a resistive divider to provide low transistor DC voltage. I like its audacious frugality!