The short answer is that I don't know, but here's some thoughts.
It's unlikely that static electricity is the key. The different procedures you name will change the static charges in very different ways, so it's hard to see why all would work if static were important.
Perhaps little rough spots on the surface interfere with the reading. Some of the procedures you mention could rub off bits of dirt and others could wash them off. Here's a wild guess about how plastic bags might work. These contain plasticizer- small molecules not well stuck to the polymer. The plasticizer can leak out- a problem for plastic food containers. It may serve to lubricate rough strips.
Here's what made me think of that. A type of copper high vacuum seal was shipped in little zip-lock bags. One of my colleagues worried that the copper might become coated with plasticizer, which could evaporate, slightly contaminating the vacuum. So he went to great lengths to clean the seals. Then they didn't work well at all. His guess that they became coated with plasticizer in the bag was right. It turned out, however, that the plasticizer was helping seal microscopic leaks at rough spots.
Mike W.
I had a problem with a magnetic strip card I had left out in the sun on my car's dashboard, and the plastic card warped and curled up on the edges. Running this card through a strip reader didn't work because the strip did not come in contact with the read head all the time. Sometimes it help if I used my hands to uncurl it a bit (very difficult to get it flat enough to read properly, and it proceeded to curl back up over time). One thing that could be happening above is that if a card is warped or bent, even just a tiny bit, it can lift off of the read-write head when read. If the card is more flexible, then it can bend back closer to its original shape when it is pulled through a narrow slot. Warming up the card a bit will make it more flexible. Many of the operations you describe above (especially rubbing it on a sweater) will warm the card up just enough to make it more flexible. I'm not sure how the plastic bag helps, but perhaps just handling the card with warm hands will help.