Sounds a lot like the OnTrac carrier in the Bay Area. One time they left a package for me at the Subway next to my building.
I stopped using Amazon same-day shipping (even when offered for free!) because it almost always used OnTrac and I would have about a 50/50 shot of actually getting the item the same day.
I've stopped getting any expiedated deliveries from Amazon via OnTrac sometime in the last year in SF proper. I think they've shifted it to in-house logistics (I think via Prime Now ICs or via Prime Fresh trucks).
UPS in the Bay Area has "pick up points" for packages. One was a gas station down the road from me. I had ordered a $500 product so I was glad it wasn't on my patio until 7pm (got to the gas station at 730p), but it was unclear where the clerk was storing packages besides under the counter.
They use LSO around here for same day and it's been pretty unreliable. On the bright side I've gotten a few months of prime and about $100 in credit back.
I stopped using Amazon same-day shipping (even when offered for free!) because it almost always used OnTrac and I would have about a 50/50 shot of actually getting the item the same day.