As the tag of your question shows, your question is about electrostatics.
Lightning strikes can occur from cloud to cloud, and from cloud to ground. As you point out, when objects are electrostatically charged (with opposite charges) they are attracted to each other. Best known example: rub a full head of hear with a balloon, and the balloon and the hair will be attracted to each other. (And they are both such poor electric conductors that they tend to remain statically charged for quite a while.)
So I think your question is a good one. If a cloud becomes electrostatically charged, then why isn't it pulled all the way down to the ground?
Let me first discuss the everyday experience that you mention, the little spark that may jump when your hand is not at the same electrostatic potential as the thing you are touching. There is actually only a very small electrostatic charge involved there. The little spark startles so much because your fingers are very sensitive to it. The cells of the nervous system use the tiniest of flow of ions across membranes to transmit signals from cell to cell. Very very little is enough to trigger that signal pathway. In the case of the little spark the actual electrostatic charge is very small, I'm sure the corresponding electrostatic attraction force is way too small to be noticable.
Let me present an educated guess here.
Clouds are buoyant. I think it's actually quite hard to make a cloud descend. Let's assume that when electrostatic charge builds up between a cloud and the ground there is a significant electrostatic force. Let's assume that makes that cloud descend somewhat. As that cloud descends it enters more dense air, so it experiences more buoyancy force. That makes it hard for that cloud to descend further.
Conversely, when a cloud finally loses a lot of charge by landing a lightning strike, will that make that cloud immediately ascend, as it suddenly experiences less electrostatic force. Again, I don't expect it to ascend much, because the air above it is less dense, so that cloud will have less buoyancy there.
I think it's plausible that the clouds have sufficent buoyancy to prevent being pulled all the way to the ground.
It could be that transient electrostatic forces play a significant role in atmospheric movements (during storms), but it could also be that any effects of the electrostatic forces are completely swamped by much larger general violent motions that occur during storms.