Critical in early steel belted radial tires, but I believe they overcame the problem. I still don't like to cross-switch, though. When a steel-belted tire comes apart, it can take half the vehicle off as it swipes the side of the car. That's an expensive test. With most motor belts, very little (if any) damage results when it lets go. Ditto sanding belts. They usually just break and stop exactly where they broke. (I'm sure we'll hear stories to the contrary any time now, though. ;)
Well, going off topic, I'd like to hear a real story about a car radial tak ing off half of a car. At least in the last 40 years. I reverse rotation, a nd run used tires all the time. I'm 51 years old and regularly drive on the German Autobahn. I have never seen a car radial tread break loose and flap . It gets my blood up all of these urban legends propagated by fraudster ti re sellers. My father-in-law will no longer rotate his tires front-to-back. His garage told him that the rims mate to the hubs when first installed, a nd won't be properly aligned if placed on a different hub. I asked him if t hey marked the bolt holes to make sure that the rims would go back onto the hub the way they came off. He didn't know, of course, and I'm sure they di dn't do it.
Sorry to go off on a rant, but, if we are to continue as a species, people need to learn to separate "that which is empirically and observably true" f rom "that which someone once said"