I've always believed in rotating the tires, makes them last longer, sometimes by a lot. When they crisscrossed them. Why do they now only make directional tires that they say can't be crisscrossed. Is the tires going to know? Why rotate to the same side, what good is that?
The main wear for tires comes from the front end. This is due to two reasons. First, this is the turning axle. The geometry changes on these tires quite a bit. When going through corners, the weight of the vehicle pushes much harder on these tires, which creates more wear than what occurs in the back. Secondly, with front wheel drive cars, which are a lot of cars on the road today, the forces employed due to forces involved with locomotion create more wear. The rear tires, by contrast, mainly just stay in line with the vehicle and get pulled along. When you change them front to back, you are trying to even the wear out between what happens front to back. This way, when the time comes, all four tires are worn evenly instead of the front tires being worn out and the back tires having another 10k miles left on them.
As far as crisscrossing tires as they used to do, the reason this isn't done anymore is not because a tire is directional (that matters too, but it's not the main reason), it's because they're radial. Way back in the day they had biased ply tires. This meant the belts which surround the tire (under the rubber) went around the tire, then had overlapping layers that went perpendicular or side to side. These tires could be ran either way without issue. With radial tires, the belts are laid crisscross or on diagonal. Once these start rolling in a particular direction, they like to stay rolling in the same direction. If they are put on the car backwards from this direction, the belts will tend to separate and destroy the tire. (Please note: You'll get people who will say they rotate them crisscross all the time without issue ... maybe they do, maybe they don't. I'm not judging.)
Because the tread pattern is designed to optimise the ejection of water for example and if you have them rotating in the wrong direction this won’t work as well.
Early design of tyres was simple : a block tread pattern, but patterns now are designed to deal with specific issues : winter tyres, mud & snow etc