I don't know what Ralph Schultz's Mills converter was built for,
but I can corroborate his suspicion that it was not built to power
a radio.  I can also answer the question, "Why not just have a radio
to plug into 110 volts?"

The earliest battery operated radios had A, B, and C batteries.  The
A battery was like a 6-volt car battery.  It ran the filaments in the
tube(s).  If you played the radio every day you would typically take
the A battery down to the blacksmith shop or hardware store and have
it charged once a week or so.  The B battery was the plate voltage,
typically 90 volts.  The C battery was for cathode bias and was
eliminated when it was realized that the same thing was accomplished
by putting a resistor between the tube cathode and ground [after tubes
with a separate cathode were developed].

By the time the rural electrification act came through, there were
already a lot of battery operated radios out there.  So, the battery
eliminator came into existence.  This was a plug-in box with two
transformers in it, one for the A and one for the B, and a rectifier
and filter for the B voltage.  Early radios were very expensive and the
eliminator was a very economical alternative to a new radio.  Last time
I looked, the C. Crane catalog still featured a battery eliminator for
early radios.

Lee Rothrock