Cheap yes, reliable no. Last time I ordered from Amazon I had to go looking for it in my neighbor's mailboxes (technically illegal for me to do that, but Amazon told me it had been delivered and yet it was not in my mailbox).
I've had horror stories no matter WHAT delivery service makes an attempt. Even those automated lockers are seriously annoying (mostly because there aren't enough of them).
I'm actually slightly amazed that the local mall doesn't talk to the various delivery companies and just "give" them an unused store front to setup an automated box for every company inside of it. I imagine the increase in traffic TO the mall would more than make up for the loss of otherwise unused dead space.
Interesting idea, but I don't think it would need to be an entire storefront. I've been to plenty of malls with entranceways that are lined with long, blank, feature-free walls. Lots of lockers could be in those places.