Why is there no proposals of folding cope cage designs yet?

This would require bearings. Do you think the Russians can afford bearings?

copevertible

Cruising for honeys in my drop-top convertible

Because shooting at the spotter is against the rules of girls tankery and the plotarmor allows a strong defence outside the tank as long as nobody says 'ITS DANGEROUS'

Drones with shaped charge goes brrr

There were, including old ones for Leo2, and in USSR (Google "защита танка Т-54 типа Шатер" and "защита танка Т-54 типа Зонтик", at that time it was intended against RPGs, of course, not drones), and here in Ukraine we had exactly the thing you proposed - folding overhead anti-drone screens on vehicles.

The answer to the question "why isn't this type of protection mass-produced", or rather "why aren't cope cages being made foldable", is that folding protection requires some resources and expertise to pull off, perhaps not that much, but still some, and with skill and resources you're better off with more conventional spaced/grate armour and ERA, otherwise it isn't worth it - not like cope cages significantly restrict the mobility of the tank in the steppes, anyway.

State actors don't implement folding screens for the same reason you see much less cope cages from ukrainians - because it's a fundamentally shitty and stupid solution. Proper solution against HEAT warheads from any direction is ERA, most russian tanks have outright crappy ERA coverage on turret roof, ours have it somewhat better. Rubber screens you see on Bulat tanks can also help, they are resin-metal mech composites and function as spaced armour to cover turret neck and areas around it. Proper solution against FPV drones is radioelectronic warfare, signal intelligence and jamming, the latter one can be done by a short range jammer mounted on a vehicle, and/or a longer range semi-stationary jammer in protected position nearby. Signal intelligence gives you the position of drone operator, then you hit him with artillery or mortars. Same way you don't exactly try making tank threads which withstand mines - you get mine-clearing vehicles and send them forward.

If you want to do spaced armour for anti-drone protection - any state actor would develop a normal spaced armour package, which conforms to the shape of the vehicle, is spaced properly, and looks like conventional spaced armour screens. Any state actor besides Russia, apparently - they did have factory-produced cope cages for some tanks, but russia is a country of geniuses which installed ERA on the sides of T-80 so lazily that the whole screen fell off on trials and got stuck in suspension, can't imagine how one could be unable to do something which is routinely done by soldiers in field repair, of course.