I asked you some years ago when you put out this wonderful gem -- if you would parametrically provide the equivalent chart for your Touring brethren. Did you ? Would you ?
@Boog -- you "know" this answer.
When a vehicle is accelerated by a turning force (as opposed to a rocket engine), there is (not nice to fool Mother Nature) an equal and opposite reaction.
Power delivered, in our case, to the rear wheel, causes the well-known squat in the rear, and in the extreme, a lifting of the front as the rear wheel attempts to rotate the bike about the rear axle. In practical terms, what we understand is that there is an effective weight transfer to the rear, so the rear benefits from more traction, and during acceleration is when you want the most traction, and because of the weight transfer, that makes sense to do in the rear.
So the tire designed for the rear, can be be advantageously biased to improve grip in that direction, as the cat has claws on the front of its paws to help it pull itself forward.
Change the vector of the acceleration to the opposite direction as we attempt to slow and stop, and the same physics is working, this time trying to remove energy from the system using the brakes to turn that energy into heat. Similarly, the brakes are attempting to rotate the bike forward over the front wheel, resulting in the well known dive when braking. This is effectively weight transfer to the front, improving traction in the front - as much as 90%. Designers of front tires can bias the the grip in the "backup" direction to improve braking. Using the example of the cat and its claws, one method a cat *could* use if it thought its rearward bias were useful for braking, is jump up in the air and swap ends, once landing, all claws would be facing aft -- still "pulling" by their original design, though in this case, pulling in the negative direction to help it stop.
So a tire designed for the rear, to pull like the cat's claws, needs to be reversed if put on the front.
As for mileage, that is not related to the direction of the tire on the axle -- more an endorsement of using that tire.