I thought it might have something to do with the dimensions neccessary vs. the frame in terms of the rod moving up and down at each end as it's attachment points revolve. Although I hadn't pictured the connection sliding, I had pictured a fixed rod from what is normally the chainwheel connecting to a similar wheel on the rear axle (say, where the cassette is normally) and driving an IGH in the hub to determine gearing. A fixed shaft that doesn't spin but rather moves back and forth as shown in the animation above. Possibly the rod could have a pivot if neccessary (if it needs to be slightly variable in length to handle the range of motion within a certain dimension? Or even to accommodate being driven by pedals w/o interfering with the crank arms?) Again, not sure about the physics implications in terms of the directions of the forces being applied and the relative efficiency.
I hadn't thought about the mounting bearings and other practical considerations.
EDIT: Having determined that this seems to be a "reciprocating rod" arrangement (or something similar) I googled up a number of patents:
So one assumes that this has been tried (
at least once) and discarded.