Then again, we have no signature required, and regularly have packages sitting on our front porch for a day or so and haven't had anything go missing.
Maybe your standards for "very secure" and "trustworthy" are extremely low.
The first one, if a package was dropped off in the lobby, the driver might as well deliver it directly into the garbage. I usually got things shipped to work, even if they were large and a hassle to get home.
The second one, our current one, all of the neighbors completely trust each other, and it's never been an issue. I ship most things home, now.
The difference is partially neighborhood (low-rent Brooklyn vs. Upper West Side), partially building size (200 units vs. 20), and partially who lives there (renters and month-to-monthers, vs. mostly condo owners.)
I saw one apartment complex this year that had a twist on the package robot concept -- there's an iPad at the door of the mail room, and you type in the code from your package, the iPad takes your photo and then unlocks the mail room door using a solenoid.
The UPS guy? Scans the barcodes on the packages, then wheels them in and drops them off on cheap metal shelves inside -- no need to pay an employee to manage the mail room 24/7. More residents/packages? Just buy a few more shelves. Resident wants to pick up a package as soon as Amazon buzzes them? No problem. Resident wants to pick up at 2am? Great.
The only problem is you have to trust your neighbors to not steal your packages.