Ive never heard of anyone saying NOT to store camper on jacks, other than there are a handful of mfgs that recommend against it or using camper off truck due to the way camper is built.
Myself I store ours on stands (though most of weight still on jacks). I built stands capable of supporting camper when stored-they have come in handy when working on it.
Just a lot more stable in high winds, going in & out as mentioned, I hate seeing it or feeling bob around. Also as extra support for the water tank (basically sets on floor hung from 1x2s) that is usually stored full. I just see it as taking some of the stress of hanging from frame and jack mounts. That and when the next earthquake hits maybe it wont walk 12" across the pad :0
When off loaded camping I generally dont do anything other than lower as far as it will go. Questionable ground I do use some small stands to stabilize & for more contact. Loss of support on one of the front jacks whether frame failure, leg buckle, rain washing out the sand were parked on or simply ground squirrel borrowing and shes going over, period. Regardless if I acknowledge possibility happening or not.
If your camper frame & jacks and the ground it sets on are trust worthy there is no reason not to store on the jacks. (other than mfg exceptions). And no reason to be uncomfortable.