FWIW, since I don't have an aeroponic cloner, your logic sounds good to me. In the humid climate under the lid i find it hard to believe the cuttings would dry out running as you suggested, and increase oxygen makes sense as well.
I once saw where someone used a ultrasonic fogger to achieve a similar effect.
Save electricity where you can, i know with all the lights, heat mats, etc I need to be conscious of such. If you had two or more cloners, you could try 5min off, one on, and so on to compare best rooting versus timing, fun.
Hope you get lots of roots.