Years ago when radial tires first came out (early-mid '70s) tire manufacturers said that radial tires "get use to" going in one direction only and that if criss-crossed like old bias ply tires, the tires would fail using a term like "belt seperation".
I've recently read that now, tire manufacturers have said that that idea now longer applies and that they can be switched side to side as well, like the old bias ply tires years ago.
I have yet to read that in "official" writing from a tire manufacturer so before doing that, play it safe and do a little homework on that as it's new to me. Since radials first came out, everyone has been going front to back only and it's also not really a problem so I see no real need to go side to side, no advantage IMO. If any tire is wearing unevenly, an alignment should be performed.