My guess is they didn't want to try and save $10 on the part; but rather there is some corporate bureaucracy requiring warranty parts to be sourced from some "internal" source (meaning, not having already been sold to a parts distributor, but rather from GM's own parts inventory). Net, it could be that your dealer had no choice but to order the warranty part through the warranty parts channel. And in that channel, the part was not available.
Now, I don't know this for sure; but I am guessing the dealer doesn't get reimbursed for parts or labor for warranty repairs unless they follow the GM designated warranty procedure...so...because the part wasn't available via the warranty parts supply chain, your situation happened. Could this be improved; one would think. But, if you look at it from GM's perspective, they are probably trying to avoid a bunch of parts resellers buying up parts, then reselling them back to GM at a profit...
Regardless, you are correct, that it affected the customer experience....and that should be a priority for a customer buying an $80k+ vehicle...