So is anyone doing a real crossing? The tires can go on either side, so long as the word "outside" is on the outside.
No.
This needlessly over-complicates the tire rotation sequence (you can no longer just jack one side of the car and move wheels front<->back, for no gain. In 30+ years of rotating and swapping tires, I've never observed any left vs. right wear variation.
The only exception to the above are track tires, that do wear lefts quicker after running (usually) clockwise all the time. Alas, this hardly applies to the discussion at hand.
a