Interesting, I'd have to go look at the laws in more detail. The cross is not required, it is used to fulfill the "lateral" restraint of the load section from what I've been told. If you had a small object they could go from the corner of the load to the corners of the trailer. I'm curious now, do you know what laws this would be in? Google hasn't been my friend.
*edit here's what I did find: http://www.fmcsa.dot.gov/content/393128
(f) Use of tiedowns.
(1) Tiedowns and securing devices must not contain knots.
(2) If a tiedown is repaired, it must be repaired in accordance with the applicable standards in paragraph (e) of this section, or the manufacturer's instructions.
(3) Each tiedown must be attached and secured in a manner that prevents it from becoming loose, unfastening, opening or releasing while the vehicle is in transit.
(4) Edge protection must be used whenever a tiedown would be subject to abrasion or cutting at the point where it touches an article of cargo. The edge protection must resist abrasion, cutting and crushing.
https://www.law.cornell.edu/cfr/text/49/393.104
The link below is for commercial loads, all have straight tiedowns for "lateral" restraint as well.
http://www.fmcsa.dot.gov/regulations/cargo-securement/drivers-handbook-cargo-securement-chapter-2-general-cargo-securement
The government's weight ratings for tiedowns is figured by deceleration in the forward direction (among other things). A straight strap would have a higher rating in the forward direction.