Opposed cone chainless progressive 24 speed gearing system using belts, has it been tried?
CVT transmissions using conical pulleys and a V-belt are common on mopeds, scooters, and very small engined cars. One of the advantages is in the name: a continuously variable transmission with literally an infinite combination of gear ratios.



Why wouldn't you want this on a bicycle? At least the system on mopeds uses centrifugal linkages to provide the "automatic" transmission and is quite heavy and requires a relatively high RPM (much faster than most bicyclists can spin their pedals). 

Furthermore, there is quite a lot of slippage caused by the v-belt especially in low gears and thus a lot of transmission power loss. For mopeds, this is actually a positive as it acts as a limited slip clutch but most bicyclists would object.

The second part of your question asks why this couldn't be done with stepped-cones. As you can tell from your photo, this would be an incredibly wide transmission. Fine for a lathe or mill (or whatever object is in the photo) but totally unsuited for most bicycles. 

tl;dr: Too heavy, too complex, and  too much power loss for bicycles.

Remember, people want their bicycles to be simple, lightweight, inexpensive, and reliable. You could get a higher efficiency, lighter system using a gates belt on a rohloff hub.