This seems like a perfectly good solution to me. You're trying to stabilize the cooler, spread the clamping force, and avoid sharp edges and wear. The part chosen seems perfectly suitable for that, albeit slightly unconventional looking.
(I say this as someone who is short $TSLA right now [and a non-practicing Mech E]; this looks perfectly reasonable to me.)
I agree that if you dug into the engineering the math probably works[1]. It's just a weird culture to be out on the floor substituting random materials in a load-bearing, if perhaps not life-safety-critical, part.
1: Compressive strength of wood perpendicular to the grain varies but you can estimate with a healthy safety margin about 200 PSI. 100x - 1000x weaker than metals, but still not zero.
I (pretty strongly) suspect that engineers were involved, rather than this being an assembly line worker floor-level decision.
The same company that erected a factory-in-a-tent (unconventional but also appropriate) to hit aggressive production targets seems like one that would consider and execute appropriate but unconventional substitutions.
I guarantee you that the materiel is not "wood" and is indeed much weaker in all relevant parameters. And I suspect that no one at TESLA has any real handle on the compressive strength of this material.
(I say this as someone who is short $TSLA right now [and a non-practicing Mech E]; this looks perfectly reasonable to me.)