I have this insane notion that keeps bugging me. Most bikes tou see nowadays have rim brakes, right?
Why not a rim drive? What I envision is a wheel rim with machined in radial grooves that in effect turn each side of it into a REALLY tall gear, and a pair of smaller spur gears (one to each side) that fit into those gear teeth snugly. Drive their shafts in counter-rotating directions, and the wheel rim between them rotates. Reserve your hub for spokes and disc (preferably) brake.
I realize there are issues with this idea, but I wonder if it could be made workable?
Alternatively, think about a vertical shaft engine rack mounted driving a wheel with a bevel gear system, an opposite side idler wheel to hold the rim firmly engaged (and possibly to serve as the actual brake pad as well).