You have this a little backwards. For maximum longevity LiPo's have a "sweet spot" somewhere between 3.6 and 4.0v, holding them at high charge voltages for storage can damage the pack, as can over-discharging the pack. As for the cutoff voltages being set where they are the packs may not have as long of a life being heavily discharged, but it shouldn't cause acute failure and I think it would be a bigger issue for the drone to quit at the end of a race than it would be to have it give what the battery pack has to give.

So don't store batteries charged, store them at about half charge and in the fridge. Heat will degrade lipos, and can make them puff.