'endorsing' Is a big word. All we know is that Martin did it, in this case. Why is for him to answer, or maybe any of the resident luthiers has insights to share.
R: the Martin shop method ... that method is used in almost ALL restorations coming from that shop, and as far as I know, he pretty much invented the technique. And MANY luthiers systematically use square, oblong and cross-grain cleats and patches.
Personally I subscribe to the diamond school - which I first learned from Arnold Schnitzer, well before Traeger's book came out - which i understand to be; reinforce along the crack/join, keep things flexible, fit and glue well, don't have 90 degree grain orientation, and don't create new stress lines. In most cases this means diamond shaped spruce cleats with grain at an angle, properly fit and neatly feathered on all facets. I
don't think cross grain gluing is wise in basses, and in most cases it can be avoided. The only cleats I have seen to fail, are ones where the grain runs perpendicular to the wood grain, or ones that are not well fit in the first place, or ones where there is insufficient glue, or chalk under the cleat.
It was David Brownell in Traeger's book who wrote, in recent history, about not cleating more than one crack with one cleat ... and with the cross-grain cleats he advocates, I totally agree. However, with the diamond cleats, not only is it much easier to avoid doing this, but the shape and grain orientation don't cause the problems he outlined. For what it is worth, even Hans "God" Weisshaar allows for cleating two or more cracks with one crossgrain cleat; and in the violin world this is probably acceptable. But in the scaled-up world of double bass luthiery, cross grain shrinkage is several orders of magnitude more of a problem.
I have become rather a zealot in regard to avoiding cross-grain glueing wherever possible, and yes, I am starting to apply this in my designs for flatback braces, as well as in all my restorations and repairs.