The original shako - pre the 1811 regs was just a straight tube, so production was more in the east to supply the Grenzers. Hence why the Hungarians were next. It was really down to production. As the infantry gave their helmets up, the decent ones went to the German cavalry.
IR4 wasn't full of Masons or officers of the Teutonic Order - it was the Vienna Hausregiment (Guard regt), so it was just fashionable - like signing up for the British Guards.