My guess is the cover plate was changed out when the other modifications were made. My understanding is it was common for dealers to take the older machines in trade then modernize them by adding electric motors and resell them. Yours hasn't been repainted but the other changes like the newer hand wheel and 1950s case that it's in would indicate that may have been what happened. It's possible the motor was mounted on the back plate so you wouldn't see any mounting holes with the plate missing too.
I'm not sure how your market is but at $25 for one needing a motor or hand crank and a missing back plate I'd probably wait for another more complete machine.
Rodney