I don't think you would get a more simple variable transmission than this.
Fitted to a little Bebe Voiturettte from the early 20's, it has a conventional propshaft with a disc attached to the end section. The steel disc is about 18" diameter. In contact with this is a wheel of similar diameter keyed to a transverse shaft.
The wheel has a friction lining material attached, this material contacts the disc face and allows the drive to feed through to the transverse shaft which has a sprocket attached, this then drives the sprocket attached to the rear axle.
The friction drive pressure is maintained by a strong coil spring loading the rear of the disc, to disconnect the drive the spring pressure is relaxed.
The clever bit is the fact that by moving the transverse wheel along the disc surface, a seamless ratio change can be achieved.
I imagine that slippage may be a problem however given the right circumstances we see that brake and clutch material is capable of transmitting a considerable amount of power.
This isn't a car in my workshop but I came across it whilst subcontracting.