speaking of odd tech on cheap bikes... who else remembers the Shimano Positron indexed shifting system? The was their first indexed rear derailleur, and the indexing took place in the rear derailleur.
I think this gets discussed in The Dancing Chain, and Frank Berto thought it would have been more successful if it hadn't been introduced on the bottom of their product line-up.
Here's an advertisement from 1975.



I don't recall whether Positron commonly came with the FFS (Front Freewheel System). This had a freewheel at the crankset in addition to the usual freewheel on the rear wheel. This allowed the user to shift while coasting up to an intersection.

Steve in Peoria