Some inventions are so important, address such a pressing need, that they get invented over and over again. So as a licensed radio nerd and enthusiast of extravagant millinery, I am pleased to introduce to you a decades-long history of people putting radios in their hats.
The first we will address is also the most recent helmet radio receiver, known in the 1950s marketplace as the Man From Mars Radio Hat:

Since transistors were still expensive, this was a tube-based radio, and prominently featured the tubes as a design element. That big hoop in the back presumably served as the antenna, while the circuitry was kept inside the hat. The inventor was Victor Hoeflich, a paper lei magnate, who dealt in novelties and party supplies. The hat was apparently a moderate success, due to a successful marketing campaign, and then faded into obscurity.
But note: Hoeflich was not the first to the patent office! Instead, one Olin Mumford of Atlanta, GA, filed his design patent for the combined hat and radio or similar article three years prior:


Why did Hoeflich’s radio hat succeed and get its own Wikipedia page, while Mumford’s failed? We could point to the unwieldy antenna of the latter, or the more streamlined design of the former, but it probably just comes down to Hoeflich having more capital than the sixteen year-old Mumford.
But that said, can you imagine better pictures existing than these of Mumford impressing people with his hat? What a king…

But even Mumford was not the first one to create a radio hat. Consider this British footage from 1931, reporting on what was supposedly a French invention:
This radio hat was reported in the August 1930 issue Modern Mechanix as being invented by a German. But before even that, this photo from the early 1920s shows a man with his radio hat:

Keep in mind, the first commercial broadcast radio station didn’t start until 1920, so this guy got it done about as early as was possible. Of course, that doesn’t preclude the possibility that people were listening to Morse code on their hats before then.