You arent missing anything, something has to suspend the car. Maybe the OP has a spring and needs shocks. If so, they wouldn't be the best looking shock but you could remove the spring and run the shock, providing the top mount unscrews like a QA-1.
Come tell this to my neighbor, he'll try and convince you that they are to the point of arguing about it. Lol
Technically they are, the assistor coil is over the damper. They are not spring preload adjustable coilovers, which most folks term as 'Coilovers' In answer to the OP question, you can run coilover dampers without springs no problem, obviously you need some form of spring to suspend the vehicle but I'm pretty sure you already have that. The only negative I can see is the aesthetics of having a threaded body, If they're hidden or you aren't bothered by looks then go for it!!
Air Shocks- the kind Back in the seventies, that would pound their way through the trunk floor on tri-five Chevys.
Back in the 70s when I worked at the gas station, this style of shock was called "overload shocks". the intended use was to add additional weight support to the rear of the car or truck. They were often bought to lift the rear a bit when the rear springs were getting weak, or if the car was expected to have to carry extra weight (like many station wagons did). Overload shocks could be pretty hard on the shock mounts. Shocks were not designed to support the vehicle weight. Yes, these were what we called coil over shocks. Their intended use was to eliminate the original coil (in most cases) springs. These started to become popular in the late 1970s. The advantages were lighter weight (especially after the original springs were eliminated), and most had the ability to be adjusted for ride height. Most were used on street rods or off street race cars. The disadvantage was they often required extra mounting bracket reinforcement. There were also McPherson struts that have the spring mounted above the shock, which many mistakenly call "coil over shocks" as well. These were what the original coil over shocks (the 2nd grouping) were designed from.
I do have chassis eng. springs on it , I bought the coil over for a better ride and handling ... 40 Ford pick up