I've definitely seen KF cars with that radio that did not have the footswitch installed. Whether it was because a dealer got lazy and didn't install it, or if it was just left behind when a radio was harvested from a parts car I don't know but I've seen cars without it.
I was not aware that there were separate units for Kaiser and Frazers in the beginning. I know the ones installed in the Kaiser cars had the plastic button for selecting stations whereas the Frazer had a chrome button which was part of the dashboard motif. My '48 Frazer standard did not have a factory radio but that button could be pressed in so the cars were equipped and ready if someone decided they wanted to install one. The installation instructions mention this.
I know AZ_HJ sent me one last year that had a different looking dial face (gold with blue or clear numbers as shown).
I saw one with that same type dial face in that '47 Frazer Manhattan at Sublett in 2012.
Was that the difference?
The one that's in my '52 Henry J had a very short shaft on the push button. I later replaced it with the longer one so I could install an original plastic button on it. I assumed the shorter shaft button on it was likely because it was intended for a Frazer which used that chrome dash button instead. But looking at the above picture, it clearly has the long shaft on the button. Maybe mine had been repaired before, it was 50 years old when I got it so you can't assume it hasn't been worked on. The dial face on mine is the typical one you see so I don't know what to think about it. Here it is -