My basic question is, what would a fast lens with a huge zoom range look like?
This question has been asked and answered for photographers on the ground - the answer was basically (rightfully) "no one would ever pay for it or be willing to lug it around." But what if those limitations were removed? Image you're building a spacecraft for inspecting other spacecraft... you'd want a wide angle for target acquisition and/or proximity operations, you would need a large zoom for imaging details, and you'd need a fast aperture to get good images of the shaded side of the target (and since space radiation will significantly reduce the available ISO of your sensor). Changing lenses robotically wouldn't be an option due to the risk of contaminating your sensor or lens elements (reference here). Budget for a piece of hardware like this could easily be tens of millions of dollars, and the mass of the lens might be worth it (compared to simply having a second camera, doubling the risk of camera failure). A real example of a project working this problem is here.
So, what would that eventual lens look like? Let's baseline a full frame sensor to start with.