It's not great to leave the kite in the chute without a cover on it. If we are sailing the next weekend we will leave the kite chute but we've got a full cover that goes over the whole chute, and keeps it nicely protected. If its not in the chute we just put it in the bag as flaking a kite supposedly doesn't really gain you anything.
There are quick and simple ways to rig a kite so that it only takes 5-10 mins.

Rigging from scratch isnt too bad either when your used to it, if you set to it could be done in 30 mins.