As I recall, this historically was the standard. In handwriting, the ligature could be and was placed naturally. In professional printing with moveable type, the ligature could be included in the typeset. Only once typewriters were invented and couldn't spare a key for every ligature did the sequential style appear and the British and American styles diverge.
This seems like it ought to be possible on a typewriter -- or at least, one with a true backspace. I'm not sure if the backspace was an advanced/late feature, though. It seems pretty simple, but mechanical parts are pretty fiddly I guess.
