"Radio Lamp Company of America"? Very specific name. Cool that they were able to fit all that in the base of a semi-normal looking lamp.

Yeah, it was pretty amazing for its time. Imagine if they made a fluorescent version with the ballast and starter in the base alongside the radio. I dunno, it's pretty cramped in there, I think they might have to put the gear in the space in the stem, above the radio.
EDIT, also there would probably also have to be some pretty aggressive filtering to overcome the 60 hz hum.

Ter was also a similar idea from the 20s that used a bright emitter tube as both the tube in a single-tube receiving circuit and the bulb. It was said to give enough light to read by.

Those things used tungsten filaments and had to run almost as hot as a normal lamp of the day, to give a tiny bit of emission. Some light would be blocked by the electrodes but otherwise it would indeed be bright enough to read by.

Yeah, that is freaky. I wonder if bright emitter vacuum tubes were ever used for lighting as well as, well, doing the usual tube things; a big transmitter tube could probably light a large room.

There were also gramophone lamps. http://www.douglas-self.com/MUSEUM/COMMS/oddgram/oddgram.htm#lampRead the whole page too if you want, and also just look at the whole Museum of Retrotech on his site. This Self person is cool.