It does exist, in the form of a CVT and controller invented by a company called NuVinci. I built a cruiser bike with the manual CVT version years ago. It worked but the hub was very heavy. If you were stopped in high gear and you pushed down on the pedal really hard to start going it would occasionally slip. Once you got going it was pleasant to use but don't expect to win any races.

They must not have sold very many of them because Fallbrook-NuVinci went into chapeter 11 and enviolo bought the tech.

https://enviolo.com/products/