I don't remember exactly when the X-ray machines were removed from shoe shops, but I doubt that it was earlier than 1960, perhaps later.Heck I don't remember that.
I suspect that Clarks were probably one of the main culprits because, if I recall correctly, they were one of the few companies which offered children's shoes in varying widths, and one of the main ('intended', rather than 'playing'!) purposes of the machines was to determine whether the shoes were wide enough!
Kind Regards, John