Excellent helmets folks! My thought would be that the felt helmet was found to be too weak for the feldzeichen, or that there was some problem with rusting on the 'loop' holding it in place (?) or maybe just became a case of a one-piece felt body eliminating that bit of work sewing in a slot to hold the badge. (?)
If it was added, it was the soldier who did so IMHO. After all, it lends a distinctive appearance that some might have desired.