I don't cross straps, either.
I did a little experiment. I loaded a 2003 Corvette into the top front slot of my Race Car Hauler. We tied it down front to back, no crossing of the straps. Left here (St Paul) and drove to Charlotte NC. Inspected the car several times on the way. We noticed the car had slid side to side up to 1.5 inches. You could see the Aluminum Floor shined up where the tires were sliding side to side. Nothing front to back. And the straps were tight.
We scuffed up the floor and crossed them on the return trip. The Car did not move.
Now keep in mind The car is basically 9 1/2 feet off the ground on the upper deck so any side to side movement is amplified up that high off the road. The smooth Aluminum Floor didn't help the situation either.
My Crew and I were having the same discussion about strapping vehicles at the time. Our issue was taking the load off of our new Penske Racing Shocks.
It was some time after that I had my buddy, MN State Patrol CVI (Commercial Vehicle Inspector) take a look at how we were tying down. He demanded crossing the Straps front and back just for this reason.
About 2-3 years after that we were heading back from Iowa and I got a call from one of my Racing buddies who left a couple of hours before us. He lost control of his Dually pulling a 26 foot tag down a hill at 65 MPH. His Truck and Trailer did a complete 360 and went down an embankment backwards after going through a Cable Guard Rail. Truck and Trailer were both totaled. The Cables had cut right through.
Once the wrecker got it pulled back up he was able to drive the car out of the trailer into my Trailer at a Truck Stop about 3 miles north. His car never moved.
His Nitrous Bottle were all over the place, his Rupp Roadster got damaged and his tool box was ripped from the floor. But his 69 Chevelle was not damaged at all in all in the upset.
We are all free to do as we please...me I'll be crossing straps and chains.