Retired Big Tire Company employee here. So, here's the deal, studies have shown that for safety, the tires with the better tread should be on the rear. I was able to see this for myself on a circle track with water being dumped on it. Drove two cars, first car had brand new set of tires with the rear tires slightly sanded down to simulate wear. Second care had the reverse setup, "worn" tires on the front. On the tract with the first car tasked to drive as fast as possible. The rear would break free in an instant with little time for the average driver to respond. The second car (worn tires on the front) you could feel the rear start to break free, but you had enough time to let off the accelerator and regain control.
It does not matter whether the vehicle is a front wheel or rear wheel drive. The cause is due to what is called bump steer. The front wheels in a turn are pointing in the direction the vehicle is moving. The rear tires are not. As the front moves in the direction of the turn, a twisting motion is caused in the tire footprint (tire contact area with the pavement), that twisting of the tire eventually causes the tire to break contact (the bump) with the road, then reestablished when the tire is then more or less pointing (the steer) in the right direction. This is repeated throughout the turn, hence "bump steer". The more worn the tire, the least likely it is to reestablish friction contact with the road.
So that would mean that you would only rotate the tires if the front tires for some reason have better tread than the rear. In my experience, my 97 Expedition front tires would wear faster than the rears, so I never rotated the tires. I usually found that by the time the front tires were due to be replaced, the rear tires were actually still in pretty good shape. I would then buy two new tires of the same brand and model. move the rear tires to the front and the new tires on the rear. During the 25 years I had that Expedition, I still got good mileage out of the tires, only had to buy two tires instead of four at a time. Sometimes I would see a good sale on that brand and model tire, buy two of them and keep in the garage till I needed them.
By the way, that tire rotation diagram came out in the fifties.